

A181306


Number of 2compositions of n having no increasing columns. 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, 1, 3, 7, 18, 44, 110, 272, 676, 1676, 4160, 10320, 25608, 63536, 157648, 391152, 970528, 2408064, 5974880, 14824832, 36783296, 91266496, 226449920, 561866240, 1394099328, 3459031296, 8582528768, 21294921472, 52836837888, 131098461184
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OFFSET

0,3


COMMENTS

Also, number of 2compositions of n that have no odd entries in the top row. 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.
a(n)=A181304(n,0).


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..29.
Index entries for linear recurrences with constant coefficients, signature (2, 2, 2).


FORMULA

G.f. =(1+z)(1z)^2/(12z2z^2+2z^3).
a(0)=1, a(1)=1, a(2)=3, a(3)=7, a(n)=2*a(n1)+2*a(n2)2*a(n3) [From Harvey P. Dale, Mar 07 2012]


EXAMPLE

a(2)=3 because we have (1/1), (2/0), and (1,1/0,0) (the 2compositions are written as (top row / bottom row).
Alternatively, a(2)=3 because we have (0/2),(2,0), and (0,0/1,1) (the 2compositions are written as (top row/bottom row)).


MAPLE

g := (1+z)*(1z)^2/(12*z2*z^2+2*z^3): gser := series(g, z = 0, 35): seq(coeff(gser, z, n), n = 0 .. 32);


MATHEMATICA

CoefficientList[Series[((1+x)(1x)^2)/(12x2x^2+2x^3), {x, 0, 30}], x] (* or *) Join[{1}, LinearRecurrence[{2, 2, 2}, {1, 3, 7}, 30]] (* Harvey P. Dale, Mar 07 2012 *)


CROSSREFS

Cf. A181304.
Sequence in context: A262321 A182995 A027967 * A178035 A000226 A291734
Adjacent sequences: A181303 A181304 A181305 * A181307 A181308 A181309


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Oct 13 2010


EXTENSIONS

Edited by N. J. A. Sloane, Oct 15 2010


STATUS

approved



