A192857 Number of matchings in the n-web graph.

4, 3, 23, 93, 439, 1988, 9107, 41583, 190047, 868341, 3967828, 18130335, 82844095, 378544117, 1729703523, 7903633148, 36114524127, 165020163823, 754036089983, 3445460307689, 15743539192644, 71937855657915, 328709765539959, 1501992365110237, 6863139770575695, 31360137777380788

Offset

0,1

Comments

Extended to a(0)-a(2) using the recurrence.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100 (corrected by Ray Chandler, Jan 19 2019)

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Web Graph

Wikipedia, Hosoya index

Index entries for linear recurrences with constant coefficients, signature (3,7,1,-1).

Formula

G.f.: (1+x)*(4 - 13*x - x^2)/(1 - 3*x - 7*x^2 - x^3 + x^4).

Mathematica

LinearRecurrence[{3, 7, 1, -1}, {4, 3, 23, 93, 439}, 30] (* Eric W. Weisstein, Mar 09 2016; amended for a(0) by Georg Fischer, Apr 03 2019 *)
Table[RootSum[1 - # - 7 #^2 - 3 #^3 + #^4 &, #^n &], {n, 0, 30}] (* Eric W. Weisstein, May 25 2017; amended for a(0) by Georg Fischer, Apr 03 2019 *)
RootSum[1 - # - 7 #^2 - 3 #^3 + #^4 &, #^Range[0, 30] &] (* Eric W. Weisstein, Oct 03 2017 *)
CoefficientList[Series[(4-9x-14x^2-x^3)/(1-3x-7x^2-x^3+x^4), {x, 0, 30}], x] (* Eric W. Weisstein, Oct 03 2017 *)

Prog

(PARI) polsym(x^4 - 3*x^3 - 7*x^2 - x + 1, 30) \\ Joerg Arndt, May 26 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)*(4-13*x-x^2)/(1-3*x-7*x^2-x^3+x^4) )); // G. C. Greubel, Jan 06 2019
(Sage) ((1+x)*(4-13*x-x^2)/(1-3*x-7*x^2-x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 06 2019

Crossrefs

Sequence in context: A052039 A243661 A035048 * A286671 A288434 A288011

Adjacent sequences: A192854 A192855 A192856 * A192858 A192859 A192860

Keyword

nonn

Author

Eric W. Weisstein, Jul 11 2011

Extensions

Redefined to include all web graphs, a(9)-a(25) from Andrew Howroyd, Mar 08 2016

Extended to a(0)-a(2) using recurrence by Eric W. Weisstein, May 26 2017

Status

approved