A121639 Number of 2-cell columns in 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.

0, 1, 5, 25, 147, 996, 7668, 66264, 635976, 6717600, 77482080, 969338880, 13076778240, 189261999360, 2925629280000, 48111515827200, 838731380659200, 15451544605593600, 299960798422118400, 6120505381423104000

Offset: 1

Author

Emeric Deutsch, Aug 14 2006

Keywords

• nonn

Comments

a(n)=Sum(k*A121637(n,k), k=0..n-1).

Examples

			a(2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes and only the vertical one has one 2-cell column.
		

References

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

Crossrefs

Cf. A121637, A121555.

Programs

Maple

a[1]:=0: a[2]:=1: a[3]:=5: for n from 4 to 43 do a[n]:=n*a[n-1]+(n-1)!-(n-3)! od: seq(a[n],n=1..23);

Formula

a(1)=0, a(2)=1, a(3)=5, a(n)=na(n-1)+(n-1)!-(n-3)! for n>=4.

Conjecture D-finite with recurrence a(n) +(-2*n+1)*a(n-1) +n*(n-2)*a(n-2) +(2*n-7)*a(n-3) -(n-3)*(n-5)*a(n-4)=0. - R. J. Mathar, Jul 22 2022