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A287497 Number of maximal matchings in the n-web graph. 1
1, 9, 22, 53, 166, 432, 1212, 3341, 9175, 25364, 69829, 192560, 530830, 1463170, 4033687, 11119101, 30651528, 84495213, 232922084, 642082488, 1769987094, 4879211973, 13450215173, 37077354584, 102208799091, 281752521488, 776689338352, 2141050324382 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Extended to a(1)-a(2) using the formula.
LINKS
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
Eric Weisstein's World of Mathematics, Web Graph
FORMULA
a(n) = a(n-1)+4*a(n-2)+3*a(n-3)-2*a(n-4)+a(n-6).
G.f.: (x*(-1-8*x-9*x^2+8*x^3-6*x^5))/(-1+x+4*x^2+3*x^3-2*x^4+x^6).
MATHEMATICA
LinearRecurrence[{1, 4, 3, -2, 0, 1}, {1, 9, 22, 53, 166, 432}, 20]
Rest @ CoefficientList[Series[(x (-1 - 8 x - 9 x^2 + 8 x^3 - 6 x^5))/(-1 + x + 4 x^2 + 3 x^3 - 2 x^4 + x^6), {x, 0, 20}], x]
Table[RootSum[-1 + 2 #^2 - 3 #^3 - 4 #^4 - #^5 + #^6 &, #^n &], {n, 20}]
RootSum[-1 + 2 #^2 - 3 #^3 - 4 #^4 - #^5 + #^6 &, #^Range[20] &] (* Eric W. Weisstein, Dec 30 2017 *)
PROG
(Magma) I:=[1, 9, 22, 53, 166, 432]; [n le 6 select I[n] else Self(n-1)+4*Self(n-2)+3*Self(n-3)-2*Self(n-4)+Self(n-6): n in [1..30]]; // Vincenzo Librandi, Sep 03 2017
CROSSREFS
Sequence in context: A250730 A251285 A197498 * A232024 A327150 A264651
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, May 25 2017
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)