cp's OEIS Frontend

A121752 Number of columns ending at an odd 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 A121752 #4 Jul 26 2022 11:29:39
%S A121752 1,2,7,39,235,1746,14166,132408,1341432,15148080,183764880,2435607360,
%T A121752 34406268480,523839899520,8444375452800,145266278169600,
%U A121752 2631329637350400,50481429165619200,1015073771517388800
%N A121752 Number of columns ending at an odd 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 A121752 a(n)=Sum(k*A121697(n,k),k=0..n).
%D A121752 E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
%D A121752 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121752 Recurrence relation: a(n)=(2n-3)a(n-1)-(n-1)(n-3)a(n-2)+(n-2)!(n*floor(n/2)-(n-2)*floor((n-1)/2)-1); a[1]=1, a[2]=2.
%F A121752 Conjecture D-finite with recurrence (-460*n+1223)*a(n) +(460*n^2+460*n-5569)*a(n-1) +(460*n^3-3826*n^2+7853*n+1313)*a(n-2) +(-460*n^4+1840*n^3+5501*n^2-31045*n+31726)*a(n-3) +(1223*n^4-13205*n^3+45787*n^2-51389*n+558)*a(n-4) -2*(426*n-1111)*(n-6)*(n-4)^2*a(n-5)=0. - _R. J. Mathar_, Jul 26 2022
%e A121752 a(2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 0 and 2 columns ending at an odd level, respectively.
%p A121752 a[1]:=1: a[2]:=2: for n from 3 to 23 do a[n]:=(2*n-3)*a[n-1]-(n-1)*(n-3)*a[n-2]+(n-2)!*(n*floor(n/2)-(n-2)*floor((n-1)/2)-1) od: seq(a[n],n=1..23);
%Y A121752 Cf. A121697, A121754.
%K A121752 nonn
%O A121752 1,2
%A A121752 _Emeric Deutsch_, Aug 23 2006