A121749 Number of deco polyominoes of height n, consisting only of columns of odd length. 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, 2, 6, 16, 66, 246, 1248, 5976, 36120, 210480, 1479600, 10140480, 81340560, 640367280, 5773662720, 51312240000, 513773124480, 5085768280320, 55995414048000, 610811823283200, 7334879610643200, 87402605773190400

Offset

1,3

Comments

a(n)=A121748(n,0).

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..23.

Formula

Recurrence relation: a(n)=floor(n/2)(a(n-1)+a(n-2)) for n>=3, a(1)=a(2)=1.

D-finite with recurrence +4*a(n) -2*a(n-1) +(-n^2-n+4)*a(n-2) +2*(-n+2)*a(n-3) +(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 26 2022

Example

a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes and only the horizontal one consists only of columns of odd length.

Maple

a[1]:=1: a[2]:=1: for n from 3 to 26 do a[n]:=floor(n/2)*(a[n-1]+a[n-2]) od: seq(a[n], n=1..26);

Crossrefs

Cf. A121746, A121748.

Sequence in context: A150032 A373452 A283420 * A009386 A009605 A009681

Adjacent sequences: A121746 A121747 A121748 * A121750 A121751 A121752

Keyword

nonn

Author

Emeric Deutsch, Aug 20 2006

Status

approved