

A276033


Number of generalizations of the partition 1^n with all elements taken modulo 2.


1



1, 2, 3, 6, 8, 17, 22, 50, 64, 154, 196, 493, 625, 1626, 2055, 5487, 6917, 18851, 23713, 65703, 82499, 231725, 290511, 825399, 1033411, 2964951, 3707851, 10728256, 13402696, 39065521, 48760366, 143047486, 178405156, 526399066, 656043856, 1945668346, 2423307046
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Consider the ranked poset L(n) of partitions defined in A002846, and take the elements of each node modulo 2, collapsing two equivalent nodes into 1. Then a(n) is the total number of paths of all lengths 0,1,...,n1 that start at any node in the poset and end at 1^n.
Oddindexed terms are the partial sums of Catalan numbers: A014138. Evenindexed terms a_{2n} are C_n (the nth Catalan number) less than the following oddindexed term.
Originally this entry had a reference to a paper on the arXiv by Caleb Ji, Enumerative Properties of Posets Corresponding to a Certain Class of No Strategy Games, arXiv:1608.06025 [math.CO], 2016. However, this article has since been removed from the arXiv.  N. J. A. Sloane, Sep 07 2018


LINKS

Table of n, a(n) for n=1..37.


CROSSREFS

Cf. A276032, A014138.
Sequence in context: A324737 A057574 A198296 * A327018 A329128 A330442
Adjacent sequences: A276030 A276031 A276032 * A276034 A276035 A276036


KEYWORD

nonn


AUTHOR

Caleb Ji, Aug 17 2016


STATUS

approved



