A121695 Number of odd-length first columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

1, 1, 3, 15, 57, 423, 2457, 22743, 178857, 1998423, 19774377, 259643223, 3093367977, 46722798423, 650703531177, 11118365780823, 177186743211177, 3379687537748823, 60644049519531177, 1277452054977620823

Offset

1,3

Comments

a(n)+A121696(n)=n!

References

E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.

E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29- 42.

Links

Table of n, a(n) for n=1..20.

Formula

a(n)=a(n-2)+(n-2)!(n*floor(n/2)-1) for n>=3; a(1)=a(2)=1.

Conjecture D-finite with recurrence a(n) +a(n-1) -n*(n-2)*a(n-2) -(2*n-3)*(n-2)*a(n-3) -(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 22 2022

Maple

a[1]:=1: a[2]:=1: for n from 3 to 23 do a[n]:=a[n-2]+(n-2)!*(n*floor(n/2)-1) od: seq(a[n], n=1..23);

Crossrefs

Cf. A121696.

Sequence in context: A218804 A125673 A123007 * A343994 A017949 A263173

Adjacent sequences: A121692 A121693 A121694 * A121696 A121697 A121698

Keyword

nonn

Author

Emeric Deutsch, Aug 17 2006

Status

approved