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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<=n-1; a deco polyomino is a directed column-convex 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are the factorials (A000142). Sum(k*T(n,k),k=0..n-1)=A134437(n).

REFERENCES

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=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(n-1,1,t)+x(1+(n-2)t)Q(n-1,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[n-1])+x*Q[n-1]+(n-2)*t*x*Q[n-1]) 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..n-1) 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

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Last modified January 16 15:21 EST 2021. Contains 340206 sequences. (Running on oeis4.)