A121553 Total area 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, 20, 122, 874, 7164, 65988, 674064, 7558416, 92276640, 1218255840, 17293495680, 262656570240, 4250077896960, 72992067321600, 1326101675673600, 25410150701107200, 512158576546713600, 10832221231772774400

Offset: 1

Author

Emeric Deutsch, Aug 08 2006

Keywords

• nonn

Comments

a(n)=Sum(k*A121552(n,k), k=n..1+n(n-1)/2).

References

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

Crossrefs

Cf. A121552.

Programs

Maple

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

Formula

a(1)=1; a(n)=n*a(n-1)+(n-1)!*[1+n(n-1)/2] for n>=2 (see Barcucci et al. reference, p. 34).

a(n)=n![n(n-1)/4 + 1/1 + 1/2 + ... +1/n]. - Emeric Deutsch, Apr 06 2008

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