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A192857
Number of matchings in the n-web graph.
1
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
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
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