

A121555


Number of 1cell columns in 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.


2



1, 2, 7, 32, 178, 1164, 8748, 74304, 704016, 7362720, 84255840, 1047358080, 14054739840, 202514376960, 3118666924800, 51119166873600, 888640952371200, 16330301780889600, 316322420114534400, 6441691128993792000
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OFFSET

1,2


COMMENTS

a(n)=Sum(k*A121554(n,k),k=0..n).
It appears that a(n) is a function of the harmonic numbers [From Gary Detlefs, Aug 13 2010]


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..20.
M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8


FORMULA

a(1)=1, a(n)=n*a(n1)+(n2)!*(n2) for n>=2.
a(n)= n!*(h(n)(n1)/n), where h(n)=sum(1/k,k=1..n) [From Gary Detlefs, Aug 13 2010]
Conjecture: (n+3)*a(n) +(2*n^27*n+4)*a(n1) (n1)*(n2)^2*a(n2)=0.  R. J. Mathar, Jul 15 2017


EXAMPLE

a(2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 2 columns with exactly 1 cell.


MAPLE

a[1]:=1: for n from 2 to 23 do a[n]:=n*a[n1]+(n2)!*(n2) od: seq(a[n], n=1..23);


CROSSREFS

Cf. A121554.
Sequence in context: A059439 A190123 A006014 * A265165 A301465 A097900
Adjacent sequences: A121552 A121553 A121554 * A121556 A121557 A121558


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Aug 08 2006


STATUS

approved



