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.

0, 1, 7, 36, 164, 700, 2868, 11424, 44576, 171216, 649520, 2439360, 9085632, 33605312, 123561536, 451998720, 1646101504, 5971400960, 21586910976, 77796897792, 279594972160, 1002326793216, 3585117623296, 12796737085440

Offset: 0

Author

Emeric Deutsch, Oct 12 2010

Keywords

• nonn

Examples

			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.
		

Links

• 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.
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).

Crossrefs

Cf. A059576

Programs

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 *)

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]