cp's OEIS Frontend

A121584 Number of cells in columns 1 and 2 of 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 A121584 #4 Jul 26 2022 11:38:40
%S A121584 1,4,18,93,569,4074,33336,306035,3111771,34708944,421407314,
%T A121584 5533007841,78125977725,1180594364966,19012215609564,325058642549919,
%U A121584 5880810783960431,112243265407073100,2254038189505807926
%N A121584 Number of cells in columns 1 and 2 of 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 A121584 a(n)=Sum(A121583(n,k),k=1..2n-2) for n>=2. a(n)=A121580(n)+A121582(n)
%D A121584 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121584 a(1)=1, a(2)=4, a(n)=[(2n-3)a(n-1)-(n-1)a(n-2)]/(n-2) + (1/2)(2n^3-9n^2+17n-16)(n-1)!/(n-2) for n>=3.
%F A121584 Conjecture D-finite with recurrence 14*(-n+1)*a(n) +(14*n^2+1731*n-6995)*a(n-1) +3*(-577*n^2+480*n+7243)*a(n-2) +2*(2781*n^2-11952*n+6004)*a(n-3) +(-5987*n^2+36181*n-54220)*a(n-4) +2*(1071*n-3433)*(n-4)*a(n-5)=0. - _R. J. Mathar_, Jul 26 2022
%e A121584 a(2)=4 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, each having a total of 2 cells in their first two columns.
%p A121584 a[1]:=1: a[2]:=4: for n from 3 to 22 do a[n]:=((2*n-3)*a[n-1]-(n-1)*a[n-2])/(n-2)+(1/2)*(2*n^3-9*n^2+17*n-16)*(n-1)!/(n-2) od: seq(a[n],n=1..22);
%Y A121584 Cf. A121580, A121582, A121583.
%K A121584 nonn
%O A121584 1,2
%A A121584 _Emeric Deutsch_, Aug 11 2006