OFFSET

1,5

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,s)=Q(n,1,s), 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(2,0)=1 and T(2,1)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 1 cells in their second columns.

Triangle starts:

1;

1,1;

1,3,2;

1,9,11,3;

1,33,43,39,4;

MAPLE

Q[1]:=t: for n from 2 to 11 do Q[n]:=expand(simplify(t*Q[n-1]+(t^n-t)/(t-1)*subs({t=s, s=1}, Q[n-1]))): P[1]:=1: P[n]:=subs(t=1, Q[n]): od: for n from 1 to 11 do seq(coeff(P[n], s, j), j=0..n-1) od; # yields sequence in triangular form

CROSSREFS

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Aug 11 2006

EXTENSIONS

Keyword tabf changed to tabl by Michel Marcus, Apr 09 2013

STATUS

approved