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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
1, 4, 20, 122, 874, 7164, 65988, 674064, 7558416, 92276640, 1218255840, 17293495680, 262656570240, 4250077896960, 72992067321600, 1326101675673600, 25410150701107200, 512158576546713600, 10832221231772774400 (list; graph; refs; listen; history; text; internal format)
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

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: A020028 A020118 A009351 * A067116 A067121 A002793

Adjacent sequences:  A121550 A121551 A121552 * A121554 A121555 A121556

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 08 2006

STATUS

approved

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Last modified June 6 13:01 EDT 2020. Contains 334827 sequences. (Running on oeis4.)