

A181307


Triangle read by rows: T(n,k) is the number of 2compositions of n having k columns with only nonzero entries (0<=k<=floor(n/2)). 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.


0



1, 2, 6, 1, 18, 6, 54, 27, 1, 162, 108, 10, 486, 405, 64, 1, 1458, 1458, 334, 14, 4374, 5103, 1549, 117, 1, 13122, 17496, 6652, 760, 18, 39366, 59049, 27064, 4238, 186, 1, 118098, 196830, 105796, 21324, 1450, 22, 354294, 649539, 401041, 99646, 9480, 271
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OFFSET

0,2


COMMENTS

Number of entries in row n is 1+floor(n/2).
Sum of entries in row n is A003480(n).
T(n,0)=2*3^{n1}=A008776(n1).
Sum(k*T(n,k),k>=0)=A054146(n1).


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..47.


FORMULA

G.f. = G(t,z)=(1z)^2/(14z+3z^2tz^2).
The g.f. of column k is z^{2k}/[(13z)^{k+1}*(1z)^{k1}] (we have a Riordan array).


EXAMPLE

T(2,1)=1 because we have (1/1) (the 2compositions are written as (top row / bottom row).
Triangle starts:
1;
2;
6,1;
18,6;
54,27,1;
162,108,10;


MAPLE

G := (1z)^2/(14*z+3*z^2t*z^2): Gser := simplify(series(G, z = 0, 15)): for n from 0 to 12 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 12 do seq(coeff(P[n], t, k), k = 0 .. floor((1/2)*n)) end do; # yields sequence in triangular form


CROSSREFS

Cf. A003480, A008776, A054146.
Sequence in context: A281307 A281417 A175353 * A008855 A181299 A181365
Adjacent sequences: A181304 A181305 A181306 * A181308 A181309 A181310


KEYWORD

nonn,tabf


AUTHOR

Emeric Deutsch, Oct 13 2010


STATUS

approved



