OFFSET
1,3
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 generating polynomial of row n is P(n,t)=Q(n,t,t), where Q(1,t,s)=t and Q(n,t,s)=tQ(n-1,t,s)+(t^n-t)Q(n-1,s,1)/(t-1) for n>=2.
EXAMPLE
T(2,2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, each having 2 cells in their first two columns.
Triangle starts:
1;
0,2;
0,1,4,1;
0,2,6,10,5,1;
0,6,16,29,34,23,11,1;
MAPLE
Q[1]:=t: for n from 2 to 9 do Q[n]:=expand(simplify(t*Q[n-1]+(t^n-t)/(t-1)*subs({t=s, s=1}, Q[n-1]))) od: for n from 1 to 9 do P[n]:=sort(subs(s=t, Q[n])): od: 1; for n from 1 to 9 do seq(coeff(P[n], t, j), j=1..2*n-2) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Aug 11 2006
STATUS
approved