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URL: https://oeis.org/A297476

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A297476
Number of maximal matchings in the 2n-crossed prism graph.
2
5, 17, 107, 553, 2635, 12569, 60611, 292737, 1412171, 6809817, 32841715, 158395537, 763938843, 3684432713, 17769791107, 85702684353, 413339234987, 1993511754617, 9614594040211, 46370641538673, 223642974511931, 1078617383866281, 5202110473022883
OFFSET
1,1
COMMENTS
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Dec 30 2017
LINKS
Eric Weisstein's World of Mathematics, Crossed Prism Graph
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
FORMULA
From Andrew Howroyd, Dec 30 2017: (Start)
a(n) = 5*a(n-1) - 4*a(n-2) + 14*a(n-3) + 4*a(n-4) + 8*a(n-5) for n > 5.
G.f.: x*(5 - 8*x + 42*x^2 + 16*x^3 + 40*x^4)/(1 - 5*x + 4*x^2 - 14*x^3 - 4*x^4 - 8*x^5).
(End)
MATHEMATICA
Table[RootSum[-8 - 4 # - 14 #^2 + 4 #^3 - 5 #^4 + #^5 & , #^n &], {n, 20}]
RootSum[-8 - 4 # - 14 #^2 + 4 #^3 - 5 #^4 + #^5 & , #^Range[20] &]
LinearRecurrence[{5, -4, 14, 4, 8}, {5, 17, 107, 553, 2635}, 20]
CoefficientList[Series[(-5 + 8 x - 42 x^2 - 16 x^3 - 40 x^4)/(-1 + 5 x - 4 x^2 + 14 x^3 + 4 x^4 + 8 x^5), {x, 0, 20}], x]
PROG
(PARI) Vec((5 - 8*x + 42*x^2 + 16*x^3 + 40*x^4)/(1 - 5*x + 4*x^2 - 14*x^3 - 4*x^4 - 8*x^5) + O(x^30)) \\ Andrew Howroyd, Dec 30 2017
CROSSREFS
Sequence in context: A349011 A143562 A261425 * A235871 A240803 A098028
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 30 2017
STATUS
approved