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A290698 Number of minimal edge covers in the n-antiprism graph. 1
2, 14, 74, 286, 1157, 4778, 19623, 80478, 330293, 1355629, 5563527, 22832914, 93707772, 384582275, 1578347684, 6477630782, 26584574434, 109104640685, 447771795953, 1837681518261, 7541951930181, 30952609765223, 127031312347552, 521343900861138 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The n-antiprism graph is well defined for n >= 3. Sequence extended to n = 1 using recurrence. - Andrew Howroyd, Aug 10 2017
LINKS
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Minimal Edge Cover
Index entries for linear recurrences with constant coefficients, signature (2, 5, 12, 11, 5, -3, -4, -1, 1).
FORMULA
From Andrew Howroyd, Aug 10 2017: (Start)
a(n) = 2*a(n-1) + 5*a(n-2) + 12*a(n-3) + 11*a(n-4) + 5*a(n-5) - 3*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9).
G.f.: x*(2 + 10*x + 36*x^2 + 44*x^3 + 25*x^4 - 18*x^5 - 28*x^6 - 8*x^7 + 9*x^8)/((1 - 3*x - 3*x^2 - 6*x^3 - 2*x^4 + 3*x^5 + 2*x^6 - x^7)*(1 + x + x^2)).
(End)
MATHEMATICA
Table[2 Cos[2 n Pi/3] + RootSum[-1 + 2 # + 3 #^2 - 2 #^3 - 6 #^4 - 3 #^5 - 3 #^6 + #^7 &, #^n &], {n, 20}]
LinearRecurrence[{2, 5, 12, 11, 5, -3, -4, -1, 1}, {2, 14, 74, 286, 1157, 4778, 19623, 80478, 330293}, 20]
CoefficientList[Series[(-2 - 10 x - 36 x^2 - 44 x^3 - 25 x^4 + 18 x^5 + 28 x^6 + 8 x^7 - 9 x^8)/(-1 + 2 x + 5 x^2 + 12 x^3 + 11 x^4 + 5 x^5 - 3 x^6 - 4 x^7 - x^8 + x^9), {x, 0, 20}], x]
PROG
(PARI)
Vec((2 + 10*x + 36*x^2 + 44*x^3 + 25*x^4 - 18*x^5 - 28*x^6 - 8*x^7 + 9*x^8)/((1 - 3*x - 3*x^2 - 6*x^3 - 2*x^4 + 3*x^5 + 2*x^6 - x^7)*(1 + x + x^2)) + O(x^30)) \\ Andrew Howroyd, Aug 10 2017
CROSSREFS
Cf. A284700.
Sequence in context: A263218 A189305 A043011 * A138156 A280392 A192809
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 09 2017
EXTENSIONS
a(1)-a(2) and terms a(7) and beyond from Andrew Howroyd, Aug 10 2017
STATUS
approved

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Last modified April 12 07:56 EDT 2024. Contains 371626 sequences. (Running on oeis4.)