cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Justin Dallant

Justin Dallant's wiki page.

Justin Dallant has authored 1 sequences.

A336631 a(n) = 1 + Max_{0<=i<=j<=k; i+j+k=n-1} a(i)*a(j)*a(k) for n>0, with a(0) = 1.

Original entry on oeis.org

1, 2, 3, 5, 9, 13, 21, 37, 55, 91, 163, 244, 406, 730, 1054, 1702, 2998, 4456, 7372, 13204, 19765, 32887, 59131, 85411, 137971, 243091, 361351, 597871, 1070911, 1603081, 2667421, 4796101, 6927701, 11190901, 19717301, 29309501, 48493901, 86862701, 130027601
Offset: 0

Views

Author

Justin Dallant, Jul 28 2020

Keywords

Comments

a(n) is the maximum number of antichains (including the empty antichain) among all posets of size n with a Hasse diagram corresponding to a ternary tree (each node has up to three children). Equivalently, a(n)-1 is the maximum number of subtrees containing the root among all ternary trees of size n.
a(n)^(1/n) converges, and the decimal expansion of the limit seems to start with 1.6296636...

Examples

			For n = 1 we have a(1) = 1 + a(0)*a(0)*a(0) = 1 + 1*1*1 = 2.
For n = 6 we have a(6) = 1 + a(1)*a(1)*a(3) = 1 + 2*2*5 = 21.
For n = 24 we have a(24) = 1 + a(4)*a(6)*a(13) = 1+9*21*730 = 137971.

Crossrefs

Ternary version of A091980.

Formula

a(n) = 1 + Max_{0<=i<=j<=k; i+j+k=n-1} a(i)*a(j)*a(k) for n>0, a(0) = 1.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.