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

0,3

Links

Harvey P. Dale, 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 Journal of Combinatorics, 28, 2007, 1724-1741.

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

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 *)
LinearRecurrence[{8, -20, 16, -4}, {0, 1, 7, 36}, 40] (* Harvey P. Dale, Nov 25 2025 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 16, -20, 8]^n*[0; 1; 7; 36])[1, 1] \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Cf. A059576.

Sequence in context: A055221 A080420 A243037 * A026018 A085354 A051198

Adjacent sequences: A181289 A181290 A181291 * A181293 A181294 A181295

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 12 2010

Status

approved