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

Author

Emeric Deutsch, Oct 12 2010

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A181299

Programs

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 *)

Formula

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