A181300 Number of columns with top entry equal to bottom entry in all the 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, 0, 1, 4, 19, 80, 328, 1304, 5084, 19512, 73976, 277688, 1033848, 3822584, 14050824, 51385720, 187095240, 678570360, 2452626312, 8837584248, 31756892552, 113831195000, 407102551688, 1452956457336, 5175872174728

Offset

0,4

Comments

a(n)=Sum(k*A181299(n,k),k>=0).

References

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.

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (7,-12,-4,12,-4).

Formula

G.f. = z^2*(1-z)^3/[(1+z)(1-4z+2z^2)^2].

Maple

g := z^2*(1-z)^3/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);

Mathematica

LinearRecurrence[{7, -12, -4, 12, -4}, {0, 0, 1, 4, 19, 80}, 30] (* Harvey P. Dale, Apr 05 2023 *)

Crossrefs

Cf. A181299

Sequence in context: A320088 A122909 A215037 * A027240 A326649 A050914

Adjacent sequences: A181297 A181298 A181299 * A181301 A181302 A181303

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 12 2010

Status

approved