cp's OEIS Frontend

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.

%I A121751 #5 Jul 26 2022 11:27:46
%S A121751 0,1,2,4,14,44,194,812,4362,22716,144282,897636,6587454,47632188,
%T A121751 396765018,3268365228,30471767658,281641273164,2906047413234,
%U A121751 29777551585092,336912811924014,3790278631556172,46662633394518258
%N 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.
%C A121751 a(n)=A121697(n,0).
%D A121751 E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
%D A121751 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29- 42.
%F A121751 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.
%F A121751 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
%e A121751 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.
%p A121751 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);
%Y A121751 Cf. A121697, A121753.
%K A121751 nonn
%O A121751 1,3
%A A121751 _Emeric Deutsch_, Aug 23 2006