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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. 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 (list; graph; refs; listen; history; text; internal format)
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 * A158118 A212137 A230295

Adjacent sequences:  A121549 A121550 A121551 * A121553 A121554 A121555

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Aug 08 2006

STATUS

approved

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Last modified April 6 20:39 EDT 2020. Contains 333286 sequences. (Running on oeis4.)