A121639 Number of 2-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.

0, 1, 5, 25, 147, 996, 7668, 66264, 635976, 6717600, 77482080, 969338880, 13076778240, 189261999360, 2925629280000, 48111515827200, 838731380659200, 15451544605593600, 299960798422118400, 6120505381423104000

Offset

1,3

Comments

a(n)=Sum(k*A121637(n,k), k=0..n-1).

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.

Formula

a(1)=0, a(2)=1, a(3)=5, a(n)=na(n-1)+(n-1)!-(n-3)! for n>=4.

Conjecture D-finite with recurrence a(n) +(-2*n+1)*a(n-1) +n*(n-2)*a(n-2) +(2*n-7)*a(n-3) -(n-3)*(n-5)*a(n-4)=0. - R. J. Mathar, Jul 22 2022

Example

a(2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes and only the vertical one has one 2-cell column.

Maple

a[1]:=0: a[2]:=1: a[3]:=5: for n from 4 to 43 do a[n]:=n*a[n-1]+(n-1)!-(n-3)! od: seq(a[n], n=1..23);

Crossrefs

Cf. A121637, A121555.

Sequence in context: A371725 A366499 A049427 * A098349 A098212 A002050

Adjacent sequences: A121636 A121637 A121638 * A121640 A121641 A121642

Keyword

nonn

Author

Emeric Deutsch, Aug 14 2006

Status

approved