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A121633 Sum of the bottom levels of the last column over 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. 4
0, 0, 1, 9, 68, 527, 4408, 40303, 403046, 4393339, 51955528, 663383135, 9102982354, 133668773755, 2092209897524, 34783032728383, 612234346270510, 11375905660965179, 222544581264066400, 4572536725690159999, 98456173247669999978, 2217126753620449439515 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) = Sum(k*A121632(n,k), k>=0).

REFERENCES

E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..449

FORMULA

a(1)=0; a(n) = n*a(n-1)+(n-1)!-1 for n>=2.

a(n)= A000254(n)- A002672(n) a(n)= n!*sum(1/k,k=1..10)- floor(n!(e-1)) [From Gary Detlefs, Jul 18 2010]

EXAMPLE

a(2)=0 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, all of whose columns start at level 0.

MAPLE

a[1]:=0: for n from 2 to 23 do a[n]:=n*a[n-1]+(n-1)!-1 od: seq(a[n], n=1..23);

MATHEMATICA

RecurrenceTable[{a[1]==0, a[n]==n*a[n-1]+(n-1)!-1}, a, {n, 20}] (* Harvey P. Dale, Dec 01 2013 *)

CROSSREFS

Cf. A121632, A000254.

Sequence in context: A133120 A194650 A048742 * A091708 A024119 A120306

Adjacent sequences:  A121630 A121631 A121632 * A121634 A121635 A121636

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 12 2006

STATUS

approved

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Last modified August 22 17:52 EDT 2019. Contains 326182 sequences. (Running on oeis4.)