A121751 Number of deco polyominoes of height n in which all columns end at an even level. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

0, 1, 2, 4, 14, 44, 194, 812, 4362, 22716, 144282, 897636, 6587454, 47632188, 396765018, 3268365228, 30471767658, 281641273164, 2906047413234, 29777551585092, 336912811924014, 3790278631556172, 46662633394518258

Offset

1,3

Comments

a(n)=A121697(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)=2floor((n-1)/2)a(n-1)-[floor((n-1)/2)floor((n-2)/2)-1]a(n-2) for n>=3, a(1)=0, a(2)=1.

Conjecture D-finite with recurrence +256*a(n) -384*a(n-1) +16*(-8*n^2+40*n-67)*a(n-2) +16*(8*n^2-54*n+87)*a(n-3) +4*(4*n^4-56*n^3+242*n^2-304*n-21)*a(n-4) +4*(-2*n^4+38*n^3-249*n^2+647*n-554)*a(n-5) +(n-4)*(n-8)*(n^2-12*n+31)*a(n-6)=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 vertical one has all of its columns ending at an even level.

Maple

a[1]:=0: a[2]:=1: for n from 3 to 26 do a[n]:=2*floor((n-1)/2)*a[n-1]-(floor((n-1)/2)*floor((n-2)/2)-1)*a[n-2] od: seq(a[n], n=1..26);

Crossrefs

Cf. A121697, A121753.

Sequence in context: A047152 A007866 A226909 * A327644 A151355 A014272

Adjacent sequences: A121748 A121749 A121750 * A121752 A121753 A121754

Keyword

nonn

Author

Emeric Deutsch, Aug 23 2006

Status

approved