A363689 Number of alternating sign matrices of size n which are indecomposable by direct and skew sums.

1, 1, 0, 1, 16, 257, 5636, 187432, 9956054, 867875816, 125861715682, 30575624363575, 12486657463326416, 8588874417105963246, 9960958211434474577452, 19489076635898035234022220, 64349049302453152886635937502, 358611453994361731825817399132622, 3373425033361375072576454177693810076

Offset

0,5

Links

Table of n, a(n) for n=0..18.

Formula

G.f.: 2*(2 - 1/ASM(x)) - ASM(x) where ASM(x) is the g.f. of A005130.

Example

a(3) = 1 because the only ASM of size 3 indecomposable by direct and skew sums is
  [0  1 0]
  [1 -1 1]
  [0  1 0]

Crossrefs

Cf. A005130, A231498, A359856.

Sequence in context: A223593 A067223 A041113 * A041482 A320362 A220742

Adjacent sequences: A363686 A363687 A363688 * A363690 A363691 A363692

Keyword

nonn

Author

Ludovic Schwob, Jun 15 2023

Status

approved