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A181306 Number of 2-compositions of n having no increasing columns. 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, number of 2-compositions of n that have no odd entries in the top row. 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.

a(n)=A181304(n,0).

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..29.

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

FORMULA

G.f. =(1+z)(1-z)^2/(1-2z-2z^2+2z^3).

a(0)=1, a(1)=1, a(2)=3, a(3)=7, a(n)=2*a(n-1)+2*a(n-2)-2*a(n-3) [From Harvey P. Dale, Mar 07 2012]

EXAMPLE

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

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

MAPLE

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

MATHEMATICA

CoefficientList[Series[((1+x)(1-x)^2)/(1-2x-2x^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

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Last modified August 18 15:59 EDT 2019. Contains 326108 sequences. (Running on oeis4.)