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A121555 Number of 1-cell columns in 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. 2
1, 2, 7, 32, 178, 1164, 8748, 74304, 704016, 7362720, 84255840, 1047358080, 14054739840, 202514376960, 3118666924800, 51119166873600, 888640952371200, 16330301780889600, 316322420114534400, 6441691128993792000 (list; graph; refs; listen; history; text; internal format)
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, 29-42.

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(n-1)+(n-2)!*(n-2) for n>=2.

a(n)= n!*(h(n)-(n-1)/n), where h(n)=sum(1/k,k=1..n) [From Gary Detlefs, Aug 13 2010]

Conjecture: (-n+3)*a(n) +(2*n^2-7*n+4)*a(n-1) -(n-1)*(n-2)^2*a(n-2)=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[n-1]+(n-2)!*(n-2) 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

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Last modified December 6 08:53 EST 2019. Contains 329788 sequences. (Running on oeis4.)