|
%I #4 Jul 22 2022 13:29:40
%S 1,1,3,15,57,423,2457,22743,178857,1998423,19774377,259643223,
%T 3093367977,46722798423,650703531177,11118365780823,177186743211177,
%U 3379687537748823,60644049519531177,1277452054977620823
%N Number of odd-length first columns 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 a(n)+A121696(n)=n!
%D E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
%D E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29- 42.
%F a(n)=a(n-2)+(n-2)!(n*floor(n/2)-1) for n>=3; a(1)=a(2)=1.
%F Conjecture D-finite with recurrence a(n) +a(n-1) -n*(n-2)*a(n-2) -(2*n-3)*(n-2)*a(n-3) -(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Jul 22 2022
%p a[1]:=1: a[2]:=1: for n from 3 to 23 do a[n]:=a[n-2]+(n-2)!*(n*floor(n/2)-1) od: seq(a[n],n=1..23);
%Y Cf. A121696.
%K nonn
%O 1,3
%A _Emeric Deutsch_, Aug 17 2006
|
