A276033 Number of generalizations of the partition 1^n with all elements taken modulo 2.

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

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 any node in the poset and end at 1^n.

Odd-indexed terms are the partial sums of Catalan numbers: A014138. Even-indexed terms a_{2n} are C_n (the n-th Catalan number) less than the following odd-indexed term.

Links

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

Caleb Ji, Enumerative Properties of Posets Corresponding to a Certain Class of Games of No Strategy, Journal of Integer Sequences, Vol. 20 (2017), Article 17.5.1.

Crossrefs

Cf. A276032, A014138.

Sequence in context: A324737 A057574 A198296 * A327018 A329128 A368687

Adjacent sequences: A276030 A276031 A276032 * A276034 A276035 A276036

Keyword

nonn

Author

Caleb Ji, Aug 17 2016

Status

approved