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A181302 Triangle read by rows: T(n,k) is the number of 2-compositions of n having k columns with distinct entries (0<=k<=n). A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n. 1
1, 0, 2, 1, 2, 4, 0, 8, 8, 8, 2, 8, 32, 24, 16, 0, 24, 56, 104, 64, 32, 4, 24, 152, 248, 304, 160, 64, 0, 64, 248, 712, 896, 832, 384, 128, 8, 64, 568, 1496, 2800, 2880, 2176, 896, 256, 0, 160, 888, 3560, 6976, 9824, 8576, 5504, 2048, 512, 16, 160, 1848, 6904, 17904 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sum of entries in row n is A003480(n).

Sum(k*T(n,k),k>=0)=A181296(n).

REFERENCES

G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European Journal of Combinatorics, 28, 2007, 1724-1741.

LINKS

Table of n, a(n) for n=0..59.

FORMULA

G.f. = G(t,z)=(1+z)(1-z)^2/[(1-z)(1-2z^2)-2tz].

G.f. of column k is 2^k*z^k*(1+z)/[(1-2z^2)^{k+1}*(1-z)^{k-1}] (we have a Riordan array).

EXAMPLE

T(2,1)=2 because we have (0/2) and (2/0) (the 2-compositions are written as (top row/bottom row).

Triangle starts:

1;

0,2;

1,2,4;

0,8,8,8;

2,8,32,24,16;

MAPLE

G := (1+z)*(1-z)^2/((1-z)*(1-2*z^2)-2*t*z): Gser := simplify(series(G, z = 0, 15)): for n from 0 to 10 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 10 do seq(coeff(P[n], t, k), k = 0 .. n) end do; # yields sequence in triangular form

CROSSREFS

Cf. A003480, A181296.

Sequence in context: A131022 A137408 A007461 * A304785 A143446 A110330

Adjacent sequences:  A181299 A181300 A181301 * A181303 A181304 A181305

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Oct 13 2010

STATUS

approved

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)