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A181329 Number of 2-compositions of n having no column with an even sum. 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. 2
1, 2, 4, 12, 32, 86, 232, 624, 1680, 4522, 12172, 32764, 88192, 237390, 638992, 1720000, 4629792, 12462194, 33544980, 90294348, 243048864, 654224230, 1761001208, 4740156528, 12759266608, 34344622042, 92446776092, 248842639740 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A181327(n,0).

Number of compositions of n into odd parts where there is 2 sorts of part 1, 4 sorts of part 3, 6 sorts of part 5, ... , 2*k sorts of part 2*k-1. - Joerg Arndt, Aug 04 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.

FORMULA

G.f.: (1-z^2)^2/(1-2z-2z^2+z^4).

EXAMPLE

a(2)=4 because we have (1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1) (the 2-compositions are written as (top row/bottom row)).

MAPLE

g := (1-z^2)^2/(1-2*z-2*z^2+z^4): gser := series(g, z = 0, 32): seq(coeff(gser, z, n), n = 0 .. 30);

MATHEMATICA

CoefficientList[Series[(1 - x^2)^2/(1 - 2 x - 2 x^2 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2014 *)

CROSSREFS

Cf. A181327.

Sequence in context: A242659 A109388 A302919 * A293007 A028860 A152035

Adjacent sequences:  A181326 A181327 A181328 * A181330 A181331 A181332

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Oct 13 2010

STATUS

approved

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Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)