A121581 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n having k cells in the second column (n>=1, k>=0). A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

1, 1, 1, 1, 3, 2, 1, 9, 11, 3, 1, 33, 43, 39, 4, 1, 153, 193, 199, 169, 5, 1, 873, 1057, 1099, 1081, 923, 6, 1, 5913, 6937, 7147, 7171, 7027, 6117, 7, 1, 46233, 53017, 54187, 54403, 54307, 53413, 47311, 8, 1, 409113, 461257, 468907, 470203, 470323, 469483, 463399

Offset

1,5

Comments

Row sums are the factorials (A000142). T(n,0)=1; Sum(k*T(n,k), k=0..n)=A121582

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..53.

Formula

The generating polynomial of row n is P(n,s)=Q(n,1,s), where Q(1,t,s)=t and Q(n,t,s)=tQ(n-1,t,s)+(t^n-t)Q(n-1,s,1)/(t-1) for n>=2.

Example

T(2,0)=1 and T(2,1)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 1 cells in their second columns.
Triangle starts:
1;
1,1;
1,3,2;
1,9,11,3;
1,33,43,39,4;

Maple

Q[1]:=t: for n from 2 to 11 do Q[n]:=expand(simplify(t*Q[n-1]+(t^n-t)/(t-1)*subs({t=s, s=1}, Q[n-1]))): P[1]:=1: P[n]:=subs(t=1, Q[n]): od: for n from 1 to 11 do seq(coeff(P[n], s, j), j=0..n-1) od; # yields sequence in triangular form

Crossrefs

Cf. A000142, A121582, A100822, A121583.

Sequence in context: A126074 A108916 A119421 * A162976 A336977 A106338

Adjacent sequences: A121578 A121579 A121580 * A121582 A121583 A121584

Keyword

nonn,tabl

Author

Emeric Deutsch, Aug 11 2006

Extensions

Keyword tabf changed to tabl by Michel Marcus, Apr 09 2013

Status

approved