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A284701
Number of maximal matchings in the n-antiprism graph.
3
2, 6, 14, 46, 137, 354, 905, 2366, 6278, 16681, 44156, 116650, 308180, 814645, 2153984, 5695102, 15056494, 39804582, 105231559, 278204561, 735502187, 1944477640, 5140687360, 13590620330, 35930023287, 94989547620, 251127430313, 663914974741
OFFSET
1,1
COMMENTS
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, May 16 2017
LINKS
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
FORMULA
From Andrew Howroyd, May 16 2017 (Start)
a(n) = 2*a(n-1) + a(n-2) + 3*a(n-4) + 5*a(n-5) + a(n-6) - 2*a(n-7) - a(n-8) for n>8.
G.f.: x*(-8*x^7 - 14*x^6 + 6*x^5 + 25*x^4 + 12*x^3 + 2*x + 2)/(x^8 + 2*x^7 - x^6 - 5*x^5 - 3*x^4 - x^2 - 2*x + 1). (End)
MATHEMATICA
LinearRecurrence[{2, 1, 0, 3, 5, 1, -2, -1}, {2, 6, 14, 46, 137, 354,
905, 2366}, 20] (* Eric W. Weisstein, May 17 2017 *)
CoefficientList[Series[x*(-8*x^7-14*x^6+6*x^5+25*x^4+12*x^3+2*x+2)/(x^8 +2*x^7-x^6-5*x^5 -3*x^4-x^2-2*x+1), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)
Table[RootSum[1 + 2 # - #^2 - 5 #^3 - 3 #^4 - #^6 - 2 #^7 + #^8 &, #^n &], {n, 10}] (* Eric W. Weisstein, May 26 2017 *)
PROG
(PARI) Vec((-8*x^7-14*x^6+6*x^5+25*x^4+12*x^3+2*x+2)/(x^8+2*x^7-x^6-5*x^5-3*x^4-x^2-2*x+1)+O(x^20)) \\ Andrew Howroyd, May 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 01 2017
EXTENSIONS
a(1)-a(2) and a(16)-a(28) from Andrew Howroyd, May 16 2017
STATUS
approved