OFFSET
0,7
COMMENTS
REFERENCES
E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
FORMULA
The row generating polynomials satisfy P(n,t)=(n-1)!+(t+n-2)P(n-1,t) for n>=1 and P(0,t)=1.
EXAMPLE
T(2,0)=1, T(2,1)=0, T(2,2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 2 columns with exactly 1 cell starting at level 0.
Triangle starts:
1;
0,1;
1,0,1;
3,1,1,1;
12,5,3,3,1;
60,27,14,12,6,1;
MAPLE
P[0]:=1: for n from 1 to 10 do P[n]:=sort(expand((n-1)!+(t+n-2)*P[n-1])) od: for n from 0 to 10 do seq(coeff(P[n], t, j), j=0..n) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Aug 12 2006
STATUS
approved