cp's OEIS Frontend

A121754 Number of columns ending at an even level 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.

%I A121754 #4 Jul 26 2022 11:32:34
%S A121754 0,1,6,31,211,1530,13086,120888,1260792,14140080,174692880,2304970560,
%T A121754 32969263680,500368821120,8139251433600,139686867532800,
%U A121754 2547638477798400,48786683184691200,986263089841612800
%N A121754 Number of columns ending at an even level 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.
%C A121754 a(n)=Sum(k*A121698(n,k),k=1..n-1).
%D A121754 E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
%D A121754 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121754 Recurrence relation: a(n)=(2n-3)a(n-1)-(n-1)(n-3)a(n-2)+(n-2)![n-2+(1/2)(1+(-1)^(n-1))(n-1)] for n>=3; a(1)=0, a(2)=1.
%F A121754 Conjecture D-finite with recurrence 16*(n+1)*a(n) +(-16*n^2-178*n+531)*a(n-1) +(-16*n^3+178*n^2-393*n-510)*a(n-2) +(16*n^4+98*n^3-1439*n^2+4222*n-3623)*a(n-3) +(-146*n^4+1479*n^3-4483*n^2+3054*n+2841)*a(n-4) +(130*n-311)*(n-6)*(-4+n)^2*a(n-5)=0. - _R. J. Mathar_, Jul 26 2022
%e A121754 a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 1 and 0 columns ending at an even level, respectively.
%p A121754 a[1]:=0: a[2]:=1: for n from 3 to 22 do a[n]:=(2*n-3)*a[n-1]-(n-1)*(n-3)*a[n-2]+(n-2)!*(n-2+(1/2)*(1+(-1)^(n-1))*(n-1)) od: seq(a[n],n=1..22);
%Y A121754 Cf. A121698, A121752.
%K A121754 nonn
%O A121754 1,3
%A A121754 _Emeric Deutsch_, Aug 23 2006