

A134436


Triangle read by rows: T(n,k) is the number of deco polyominoes of height n with k cells in the second row (0<=k<=n1; a deco polyomino is a directed columnconvex polyomino in which the height, measured along the diagonal, is attained only in the last column).


1



1, 1, 1, 1, 3, 2, 1, 7, 10, 6, 1, 16, 37, 42, 24, 1, 44, 125, 214, 216, 120, 1, 169, 465, 959, 1406, 1320, 720, 1, 895, 2199, 4469, 7880, 10476, 9360, 5040, 1, 5942, 13504, 24902, 44203, 70676, 87732, 75600, 40320
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OFFSET

1,5


COMMENTS

Row sums are the factorials (A000142). Sum(k*T(n,k),k=0..n1)=A134437(n).


REFERENCES

E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 2942.


LINKS

Table of n, a(n) for n=1..45.


FORMULA

The generating polynomial of row n is P(n,t)=Q(n,t,1), where Q(1,t,x)=x and Q(n,t,x)=xQ(n1,1,t)+x(1+(n2)t)Q(n1,t,x) for n>=2.


EXAMPLE

T(2,0)=T(2,1)=1 because the horizontal domino has no cells in the 2nd row and the vertical domino has 1 cell in the 2nd row.
Triangle starts:
1;
1,1;
1,3,2;
1,7,10,6;
1,16,37,42,24;


MAPLE

Q[1]:=x: for n from 2 to 10 do Q[n]:=expand(x*subs({t=1, x=t}, Q[n1])+x*Q[n1]+(n2)*t*x*Q[n1]) end do: for n to 9 do P[n]:=sort(subs(x=1, Q[n])) end do: for n to 9 do seq(coeff(P[n], t, j), j=0..n1) end do; # yields sequence in triangular form


CROSSREFS

Cf. A000142, A134437.
Sequence in context: A171128 A122832 A056151 * A306226 A186370 A163626
Adjacent sequences: A134433 A134434 A134435 * A134437 A134438 A134439


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Nov 30 2007


STATUS

approved



