A387585 Number of matchings in the n-Plummer-Toft graph.

32, 71, 153, 320, 651, 1297, 2536, 4883, 9277, 17424, 32399, 59717, 109216, 198367, 358065, 642736, 1147923, 2040809, 3613064, 6372139, 11198645, 19617120, 34261015, 59669821, 103653344, 179623031, 310569993, 535843424, 922685595, 1585836673, 2720815336

Offset

0,1

Links

Table of n, a(n) for n=0..30.

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

Eric Weisstein's World of Mathematics, Plummer-Toft Graph.

Index entries for linear recurrences with constant coefficients, signature (3,0,-5,0,3,1).

Formula

a(n) = 3*a(n-1)-5*a(n-3)+3*a(n-5)+a(n-6).

G.f.: x*(-32+25*x+60*x^2-21*x^3-46*x^4-13*x^5)/(-1+x+x^2)^3.

E.g.f.: exp(x/2)*(5*(325 + 238*x + 50*x^2)*cosh(sqrt(5)*x/2) + sqrt(5)*(799 + 550*x + 110*x^2)*sinh(sqrt(5)*x/2))/125 - 13. - Stefano Spezia, Sep 02 2025

Mathematica

LinearRecurrence[{3, 0, -5, 0, 3, 1}, {32, 71, 153, 320, 651, 1297}, 20]
CoefficientList[Series[(-32 + 25 x + 60 x^2 - 21 x^3 - 46 x^4 - 13 x^5)/(-1 + x + x^2)^3, {x, 0, 20}], x]

Crossrefs

Sequence in context: A100017 A135110 A228665 * A101539 A106700 A250755

Adjacent sequences: A387582 A387583 A387584 * A387586 A387587 A387588

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 02 2025

Status

approved