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A276032 Number of refinements of the partition n^1 with all numbers taken modulo 2. 1
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 (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,...,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
LINKS
CROSSREFS
Sequence in context: A181658 A251541 A325105 * A114281 A137823 A024540
KEYWORD
nonn
AUTHOR
Caleb Ji, Aug 17 2016
STATUS
approved

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Last modified April 21 19:32 EDT 2024. Contains 371885 sequences. (Running on oeis4.)