

A121553


Total area of all deco polyominoes of height n. A deco polyomino is a directed columnconvex 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
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OFFSET

1,2


COMMENTS

a(n)=Sum(k*A121552(n,k), k=n..1+n(n1)/2).


REFERENCES

E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 2942.


LINKS

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


FORMULA

a(1)=1; a(n)=n*a(n1)+(n1)!*[1+n(n1)/2] for n>=2 (see Barcucci et al. reference, p. 34).
a(n)=n![n(n1)/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[n1]+(n1)!*(1+n*(n1)/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



