OFFSET
1,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Edge Cover
Eric Weisstein's World of Mathematics, Minimal Edge Cover
Eric Weisstein's World of Mathematics, Moebius Ladder
Index entries for linear recurrences with constant coefficients, signature (1, 2, 6, 2, 2, -2, -2, -1, 1).
FORMULA
From Andrew Howroyd, Aug 04 2017: (Start)
a(n) = a(n-1) + 2*a(n-2) + 6*a(n-3) + 2*a(n-4) + 2*a(n-5) - 2*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n > 9.
G.f.: x*(1 + x)*(1 + 4*x^3 - 3*x^4)*(3 + x + x^2 - x^3)/((1 + x^2)*(1 + x + x^2 - x^3)*(1 - 2*x - 2*x^2 + x^4)).
(End)
MATHEMATICA
Table[2 Cos[n Pi/2] - RootSum[-1 + # + #^2 + #^3 &, #^n &] +
RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, #^n &], {n, 20}]
LinearRecurrence[{1, 2, 6, 2, 2, -2, -2, -1, 1}, {3, 7, 15, 59, 143, 367, 1039, 2755, 7395}, 20]
CoefficientList[Series[-(((1 + x) (-3 - x - x^2 + x^3) (-1 - 4 x^3 + 3 x^4))/((1 + x^2) (-1 - x - x^2 + x^3) (1 - 2 x - 2 x^2 + x^4))), {x, 0, 20}], x]
PROG
(PARI) Vec((1 + x)*(1 + 4*x^3 - 3*x^4)*(3 + x + x^2 - x^3)/((1 + x^2)*(1 + x + x^2 - x^3)*(1 - 2*x - 2*x^2 + x^4)) + O(x^30)) \\ Andrew Howroyd, Aug 04 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 03 2017
EXTENSIONS
a(1)-a(2) and terms a(9) and beyond from Andrew Howroyd, Aug 04 2017
STATUS
approved