A121552 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and area k (n>=1, k>=1). 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, 0, 2, 0, 0, 4, 2, 0, 0, 0, 8, 8, 6, 2, 0, 0, 0, 0, 16, 24, 28, 26, 16, 8, 2, 0, 0, 0, 0, 0, 32, 64, 96, 120, 126, 110, 82, 52, 26, 10, 2, 0, 0, 0, 0, 0, 0, 64, 160, 288, 432, 564, 658, 680, 638, 542, 416, 284, 172, 90, 38, 12, 2, 0, 0, 0, 0, 0, 0, 0, 128, 384, 800, 1376, 2072

Offset

1,3

Comments

Row n has 1+n(n-1)/2 terms, the first n-1 being 0's. Row sums are the factorials (A000142). T(n,n)=2^(n-1). Sum(k*T(n,k), k=1..1+n(n-1)/2)=A121553(n).

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..75.

Formula

The row generating polynomials are P(1,t)=t and P(n,t)=2t^n*product(2+t+t^2+...+t^j, j=1..n-2) for n>=2.

Example

Triangle starts:
1;
0,2;
0,0,4,2;
0,0,0,8,8,6,2;
0,0,0,0,16,24,28,26,16,8,2;

Maple

for n from 1 to 8 do P[n]:=sort(expand(simplify(2*t^n*product(2+sum(t^i, i=1..j), j=1..n-2)))) od: for n from 1 to 8 do seq(coeff(P[n], t, j), j=1..n*(n-1)/2+1) od; # yields sequence in triangular form

Crossrefs

Cf. A000142, A121553.

Sequence in context: A288098 A118965 A252729 * A350785 A158118 A212137

Adjacent sequences: A121549 A121550 A121551 * A121553 A121554 A121555

Keyword

nonn,tabf

Author

Emeric Deutsch, Aug 08 2006

Status

approved