A328890 Number of acyclic edge covers of the complete bipartite graph K_{n,2}.

1, 6, 18, 46, 110, 254, 574, 1278, 2814, 6142, 13310, 28670, 61438, 131070, 278526, 589822, 1245182, 2621438, 5505022, 11534334, 24117246, 50331646, 104857598, 218103806, 452984830, 939524094, 1946157054, 4026531838, 8321499134, 17179869182, 35433480190, 73014444030

Offset: 1

Author

Andrew Howroyd, Oct 29 2019

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Complete Bipartite Graph
• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Crossrefs

Column 2 of A328888.

Cf. A000225, A001787.

Programs

PARI

a(n) = {(2 + n)*2^(n-1) - 2}

PARI

Vec(x*(1 + x - 4*x^2) / ((1 - x)*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Nov 05 2019

Formula

a(n) = 2*A000225(n-1) + A001787(n).

a(n) = (2 + n)*2^(n-1) - 2.

From Colin Barker, Nov 05 2019: (Start)

G.f.: x*(1 + x - 4*x^2) / ((1 - x)*(1 - 2*x)^2).

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>3.

(End)