A387571 Number of matchings in the n-double cone graph.

3, 21, 64, 217, 671, 2052, 6119, 18001, 52288, 150429, 429243, 1216516, 3427659, 9609357, 26821696, 74576737, 206650199, 570877956, 1572754223, 4322192329, 11851475008, 32430381861, 88576465779, 241511251972, 657457204371, 1787147867397, 4851349002304

Offset

1,1

Comments

Sequence extended to a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Double Cone Graph.

Eric Weisstein's World of Mathematics, Independent Edge Set.

Index entries for linear recurrences with constant coefficients, signature (5,-5,-5,5,-1).

Formula

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

G.f.: (x*(3+6*x-26*x^2+17*x^3-4*x^4))/((1+x)*(1-3*x+x^2)^2).

Mathematica

Table[2 (-1)^(n + 1) + Fibonacci[2 n + 5] + ((5 - 3 Sqrt[5]) (3 - Sqrt[5])^n + (3 + Sqrt[5])^n (5 + 3 Sqrt[5])) n/(5 2^n) , {n, 0, 20}] // Expand
seq = LinearRecurrence[{5, -5, -5, 5, -1}, {3, 21, 64, 217, 671, 2052}, 20]
CoefficientList[Series[(3 + 6 x - 26 x^2 + 17 x^3 - 4 x^4)/((1 + x) (1 - 3 x + x^2)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A331082 A117984 A050615 * A145658 A342548 A188667

Adjacent sequences: A387568 A387569 A387570 * A387572 A387573 A387574

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 02 2025

Status

approved