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A121697 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and having k columns ending at an odd level (0<=k<=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. 3
1, 0, 1, 1, 0, 1, 2, 2, 1, 1, 4, 8, 7, 3, 2, 14, 32, 37, 23, 10, 4, 44, 142, 207, 180, 97, 38, 12, 194, 730, 1267, 1327, 911, 425, 150, 36, 812, 3810, 8104, 10387, 8876, 5257, 2222, 708, 144, 4362, 23284, 56987, 84792, 85317, 60814, 31368, 11972, 3408, 576, 22716 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Row sums are the factorials (A000142). T(n,0)=A121751 T(n,n)=A010551(n-1) for n>=1. Sum(k*T(n,k), k=0..n)=A121752(n).

REFERENCES

E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.

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=0..55.

FORMULA

The row generating polynomials P[n](t) are given by P[n](t)=Q[n](t,1), where Q[n](t,s) are defined by Q[n](t,s)=Q[n-1](s,t)+[floor(n/2)*t+floor((n-1)/2)*s]Q[n-1](t,s) for n>=2 and Q[0](t,s)=1, Q[1](t,s]=t.

EXAMPLE

T(2,0)=1, T(2,1)=0 and T(2,2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 0 and 2 columns ending at an odd level, respectively.

Triangle starts:

1;

0,1;

1,0,1;

2,2,1,1;

4,8,7,3,2;

14,32,37,23,10,4;

MAPLE

Q[0]:=1: Q[1]:=t: for n from 2 to 10 do Q[n]:=expand(subs({t=s, s=t}, Q[n-1])+(t*floor(n/2)+s*floor((n-1)/2))*Q[n-1]) od: for n from 0 to 10 do P[n]:=sort(subs(s=1, Q[n])) od: for n from 0 to 10 do seq(coeff(P[n], t, j), j=0..n) od; # yields sequence in triangular form

CROSSREFS

Cf. A000142, A010551, A121751, A121752, A121698.

Sequence in context: A199802 A297347 A342623 * A225201 A124976 A176663

Adjacent sequences:  A121694 A121695 A121696 * A121698 A121699 A121700

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Aug 23 2006

STATUS

approved

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Last modified January 26 13:09 EST 2022. Contains 350598 sequences. (Running on oeis4.)