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.

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

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.

Index entries for linear recurrences with constant coefficients, signature (2,2,0,-1).

Formula

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