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

1,2

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.

Links

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

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

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);

Crossrefs

Cf. A121552.

Sequence in context: A020118 A009351 A379202 * A067116 A347339 A067121

Adjacent sequences: A121550 A121551 A121552 * A121554 A121555 A121556

Keyword

nonn

Author

Emeric Deutsch, Aug 08 2006

Status

approved