A276032 Number of refinements of the partition n^1 with all numbers taken modulo 2.

1, 2, 3, 7, 8, 21, 22, 63, 64, 195, 196, 624, 625, 2054, 2055, 6916, 6917, 23712, 23713, 82498, 82499, 290510, 290511, 1033410, 1033411, 3707850, 3707851, 13402695, 13402696, 48760365, 48760366, 178405155, 178405156, 656043855, 656043856, 2423307045

Offset: 1

Author

Caleb Ji, Aug 17 2016

Keywords

• nonn

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,...,n-1 that start at (n mod 2)^1 and end at any node in the poset.

Odd-indexed terms are the partial sums of Catalan numbers: A014138.

Even-indexed terms are one less than the following odd-indexed 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

Crossrefs

Cf. A276033, A014138.