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
Keywords
Examples
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.
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.
Programs
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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);
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
Comments