Find a combinatorial interpretation of $ x_n = x_{n - 2} + x_{n - 3}$
$begingroup$
Let $ x_0 = 3, x_1 = 0, x_2 = 2$ and: $$ x_n = x_{n - 2} + x_{n - 3}$$
How to find a combinatorial interpretation of this equation?
One idea was to find a number of different tiles of a circle divided on $n$ unit arcs with arcs of lenght $2$ and $3$, but this obviously fails.
combinatorics
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
$endgroup$
add a comment |
$begingroup$
Let $ x_0 = 3, x_1 = 0, x_2 = 2$ and: $$ x_n = x_{n - 2} + x_{n - 3}$$
How to find a combinatorial interpretation of this equation?
One idea was to find a number of different tiles of a circle divided on $n$ unit arcs with arcs of lenght $2$ and $3$, but this obviously fails.
combinatorics
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
$endgroup$
2
$begingroup$
This is A001608 and there are some suggestions given there (though nothing I'd say was terribly compelling).
$endgroup$
– lulu
Jan 18 at 13:07
2
$begingroup$
More references and a not particularly funny cartoon are here.
$endgroup$
– lulu
Jan 18 at 13:08
2
$begingroup$
And here (though no cartoon).
$endgroup$
– lulu
Jan 18 at 13:17
add a comment |
$begingroup$
Let $ x_0 = 3, x_1 = 0, x_2 = 2$ and: $$ x_n = x_{n - 2} + x_{n - 3}$$
How to find a combinatorial interpretation of this equation?
One idea was to find a number of different tiles of a circle divided on $n$ unit arcs with arcs of lenght $2$ and $3$, but this obviously fails.
combinatorics
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
$endgroup$
Let $ x_0 = 3, x_1 = 0, x_2 = 2$ and: $$ x_n = x_{n - 2} + x_{n - 3}$$
How to find a combinatorial interpretation of this equation?
One idea was to find a number of different tiles of a circle divided on $n$ unit arcs with arcs of lenght $2$ and $3$, but this obviously fails.
combinatorics
combinatorics
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
asked Jan 18 at 13:01
greedoidgreedoid
42.2k1152105
42.2k1152105
2
$begingroup$
This is A001608 and there are some suggestions given there (though nothing I'd say was terribly compelling).
$endgroup$
– lulu
Jan 18 at 13:07
2
$begingroup$
More references and a not particularly funny cartoon are here.
$endgroup$
– lulu
Jan 18 at 13:08
2
$begingroup$
And here (though no cartoon).
$endgroup$
– lulu
Jan 18 at 13:17
add a comment |
2
$begingroup$
This is A001608 and there are some suggestions given there (though nothing I'd say was terribly compelling).
$endgroup$
– lulu
Jan 18 at 13:07
2
$begingroup$
More references and a not particularly funny cartoon are here.
$endgroup$
– lulu
Jan 18 at 13:08
2
$begingroup$
And here (though no cartoon).
$endgroup$
– lulu
Jan 18 at 13:17
2
2
$begingroup$
This is A001608 and there are some suggestions given there (though nothing I'd say was terribly compelling).
$endgroup$
– lulu
Jan 18 at 13:07
$begingroup$
This is A001608 and there are some suggestions given there (though nothing I'd say was terribly compelling).
$endgroup$
– lulu
Jan 18 at 13:07
2
2
$begingroup$
More references and a not particularly funny cartoon are here.
$endgroup$
– lulu
Jan 18 at 13:08
$begingroup$
More references and a not particularly funny cartoon are here.
$endgroup$
– lulu
Jan 18 at 13:08
2
2
$begingroup$
And here (though no cartoon).
$endgroup$
– lulu
Jan 18 at 13:17
$begingroup$
And here (though no cartoon).
$endgroup$
– lulu
Jan 18 at 13:17
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3078218%2ffind-a-combinatorial-interpretation-of-x-n-x-n-2-x-n-3%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3078218%2ffind-a-combinatorial-interpretation-of-x-n-x-n-2-x-n-3%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
This is A001608 and there are some suggestions given there (though nothing I'd say was terribly compelling).
$endgroup$
– lulu
Jan 18 at 13:07
2
$begingroup$
More references and a not particularly funny cartoon are here.
$endgroup$
– lulu
Jan 18 at 13:08
2
$begingroup$
And here (though no cartoon).
$endgroup$
– lulu
Jan 18 at 13:17