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.

1, 4, 18, 93, 569, 4074, 33336, 306035, 3111771, 34708944, 421407314, 5533007841, 78125977725, 1180594364966, 19012215609564, 325058642549919, 5880810783960431, 112243265407073100, 2254038189505807926

Offset: 1

Author

Emeric Deutsch, Aug 11 2006

Keywords

• nonn

Comments

a(n)=Sum(A121583(n,k),k=1..2n-2) for n>=2. a(n)=A121580(n)+A121582(n)

Examples

			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.
		

References

• E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.

Crossrefs

Cf. A121580, A121582, A121583.

Programs

Maple

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);

Formula

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.

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