cp's OEIS Frontend

A121753 Number of deco polyominoes of height n in which all columns end at an odd 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 A121753 #3 Mar 30 2012 17:36:11
%S A121753 1,1,2,6,16,62,230,1114,5268,30702,176226,1201638,8107464,63339702,
%T A121753 491010102,4324845834,37867131900,371275954758,3623124865986,
%U A121753 39137296073094,421150512316032,4969568447400366,58455531552960198
%N A121753 Number of deco polyominoes of height n in which all columns end at an odd 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 A121753 a(n)=A121698(n,0).
%D A121753 E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
%D A121753 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121753 Recurrence relation: a(n)=(1+2floor((n-2)/2))a(n-1)-[floor((n-1)/2)floor((n-2)/2)-1]a(n-2) for n>=3, a(1)=1, a(2)=1.
%e A121753 a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes and only the horizontal one has all of its columns ending at an odd level.
%p A121753 a[1]:=1: a[2]:=1: for n from 3 to 26 do a[n]:= (1+2*floor((n-2)/2))*a[n-1]-(floor((n-1)/2)*floor((n-2)/2)-1)*a[n-2] od: seq(a[n],n=1..26);
%Y A121753 Cf. A121698, A121751.
%K A121753 nonn
%O A121753 1,3
%A A121753 _Emeric Deutsch_, Aug 23 2006