A305777 Number of set partitions of [n] with alternating parity of elements and exactly three blocks.

1, 3, 7, 14, 30, 57, 119, 224, 460, 867, 1761, 3338, 6734, 12861, 25843, 49748, 99744, 193431, 387365, 756062, 1513138, 2969265, 5940567, 11708072, 23420228, 46317195, 92642569, 183707186, 367430742, 730111269, 1460255291, 2906227196, 5812519912, 11582124159

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (3,4,-18,1,33,-16,-18,12)

Formula

G.f.: (10*x^6 -x^5 -13*x^4 +x^3 +6*x^2-1) *x^3 / ((2*x-1) *(x+1) *(3*x^2-1) *(2*x^2-1) *(x-1)^2).

Example

a(5) = 7: 123|4|5, 12|34|5, 12|3|45, 1|234|5, 145|2|3, 1|2|345, 1|23|45.

Crossrefs

Column k=3 of A274581.

Sequence in context: A074988 A265381 A066225 * A139817 A173010 A036892

Adjacent sequences: A305774 A305775 A305776 * A305778 A305779 A305780

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 10 2018

Status

approved