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A181292 The sum of the entries in the top rows of all 2-compositions of n. 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
0, 1, 7, 36, 164, 700, 2868, 11424, 44576, 171216, 649520, 2439360, 9085632, 33605312, 123561536, 451998720, 1646101504, 5971400960, 21586910976, 77796897792, 279594972160, 1002326793216, 3585117623296, 12796737085440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

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.

FORMULA

a(n) = Sum_{k=0..n} k*A059576(n,k).

G.f.: z(1-z)/(1-4z+2z^2)^2. [Corrected by Georg Fischer, May 19 2019]

EXAMPLE

a(2)=7 because the 2-compositions of 2, written as (top row / bottom row), are (0 / 2), (1 / 1), (2 / 0), (1,0 / 0,1), (0,1 / 1,0), (1,1 / 0,0), (0,0 / 1,1) and the sum of the entries in the top rows is 0 + 1 + 2 + 1 + 0 +0 +1 + 1 + 1 + 0 + 0 = 7.

MAPLE

g := z*(1-z)/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 30): seq(coeff(gser, z, k), k = 0 .. 25);

MATHEMATICA

CoefficientList[Series[x(1-x)/(1-4x+2x^2)^2, {x, 0, 30}], x] (* Georg Fischer, May 19 2019 *)

CROSSREFS

Cf. A059576

Sequence in context: A055221 A080420 A243037 * A026018 A085354 A051198

Adjacent sequences:  A181289 A181290 A181291 * A181293 A181294 A181295

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Oct 12 2010

STATUS

approved

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Last modified May 17 19:51 EDT 2022. Contains 353778 sequences. (Running on oeis4.)