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.

0, 0, 1, 9, 68, 527, 4408, 40303, 403046, 4393339, 51955528, 663383135, 9102982354, 133668773755, 2092209897524, 34783032728383, 612234346270510, 11375905660965179, 222544581264066400, 4572536725690159999, 98456173247669999978, 2217126753620449439515

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]

D-finite with recurrence a(n) +(-2*n-1)*a(n-1) +(n^2+2*n-4)*a(n-2) +(-2*n^2+6*n-3)*a(n-3) +(n-3)^2*a(n-4)=0. - R. J. Mathar, Jul 26 2022

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 A327560 A024119

Adjacent sequences: A121630 A121631 A121632 * A121634 A121635 A121636

Keyword

nonn

Author

Emeric Deutsch, Aug 12 2006

Status

approved