cp's OEIS Frontend

A121638 Number of deco polyominoes of height n, having no 2-cell columns. 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 A121638 #7 Jul 03 2023 18:42:22
%S A121638 1,1,2,7,29,147,889,6252,50163,452356,4529812,49878095,598989496,
%T A121638 7791393260,109129383735,1637539745521,26208427321596,445652393850867,
%U A121638 8023380629061127,152470440379483009,3049854459983511047,64054967040282793114,1409361745326600931517
%N A121638 Number of deco polyominoes of height n, having no 2-cell columns. 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 A121638 a(n) = A121637(n,0).
%D A121638 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121638 D-finite with recurrence a(n)=(n-1)a(n-1)+a(n-3) for n>=3; a(1)=1, a(2)=1, a(3)=2.
%e A121638 a(2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes and only the horizontal one has no 2-cell column.
%p A121638 a[1]:=1: a[2]:=1: a[3]:=2: for n from 4 to 23 do a[n]:=(n-1)*a[n-1]+a[n-3] od: seq(a[n],n=1..23);
%Y A121638 Cf. A121637, A001053.
%K A121638 nonn
%O A121638 1,3
%A A121638 _Emeric Deutsch_, Aug 14 2006