A121580 Number of cells in column 1 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, 3, 11, 53, 317, 2237, 18077, 164237, 1656077, 18348557, 221561357, 2895986957, 40737113357, 613623026957, 9854521894157, 168083120422157, 3034505335078157, 57810369261862157, 1159018646647078157

Offset: 1

Author

Emeric Deutsch, Aug 09 2006

Keywords

• nonn
• easy

Examples

			a(2)=3 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 2 and 1 cells in their first columns.
		

Links

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

Crossrefs

Cf. A100822.

Programs

Maple

a[1]:=1: for n from 2 to 22 do a[n]:=a[n-1]+(n-1)!*(1+n*(n-1)/2) od: seq(a[n],n=1..22);

Formula

a(1) = 1, a(n) = a(n-1)+(n-1)!*(1+n*(n-1)/2) for n>=2.

a(n) = Sum_{k=1..n} k*A100822(n,k).

a(n) = (1/2)*Sum_{j=0..n+1} j! - n!. - Emeric Deutsch, Apr 06 2008

Conjecture D-finite with recurrence a(n) +(-n-4)*a(n-1) +3*(n+1)*a(n-2) +2*(-2*n+3)*a(n-3) +2*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 26 2022