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

1,2

Comments

a(n)=Sum(k*A100822(n,k),k=1..n).

References

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

Links

Table of n, a(n) for n=1..19.

Formula

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

a(n)=(1/2)Sum(j!,j=0..n+1) - 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

Example

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.

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);

Crossrefs

Cf. A100822.

Sequence in context: A351200 A000255 A318912 * A321732 A224345 A081367

Adjacent sequences: A121577 A121578 A121579 * A121581 A121582 A121583

Keyword

nonn

Author

Emeric Deutsch, Aug 09 2006

Status

approved