

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 columnconvex polyomino in which the height, measured along the diagonal, is attained only in the last column.


3



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
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OFFSET

1,3


COMMENTS

Row n has 1+n(n1)/2 terms, the first n1 being 0's. Row sums are the factorials (A000142). T(n,n)=2^(n1). Sum(k*T(n,k), k=1..1+n(n1)/2)=A121553(n).


REFERENCES

E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 2942.


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..n2) 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..n2)))) od: for n from 1 to 8 do seq(coeff(P[n], t, j), j=1..n*(n1)/2+1) od; # yields sequence in triangular form


CROSSREFS

Cf. A000142, A121553.
Sequence in context: A288098 A118965 A252729 * A158118 A212137 A230295
Adjacent sequences: A121549 A121550 A121551 * A121553 A121554 A121555


KEYWORD

nonn,tabf


AUTHOR

Emeric Deutsch, Aug 08 2006


STATUS

approved



