

A181302


Triangle read by rows: T(n,k) is the number of 2compositions of n having k columns with distinct entries (0<=k<=n). A 2composition 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
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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 Lconvex polyominoes, European Journal of Combinatorics, 28, 2007, 17241741.


LINKS

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


FORMULA

G.f. = G(t,z)=(1+z)(1z)^2/[(1z)(12z^2)2tz].
G.f. of column k is 2^k*z^k*(1+z)/[(12z^2)^{k+1}*(1z)^{k1}] (we have a Riordan array).


EXAMPLE

T(2,1)=2 because we have (0/2) and (2/0) (the 2compositions 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)*(1z)^2/((1z)*(12*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



