OFFSET
2,2
COMMENTS
The n-wheel graph is well defined for n>=4. Sequence extended to n=2 using recurrence. This gives values for a single edge and for a wheel with two spokes connected by two rim edges. - Andrew Howroyd, Aug 04 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..200
Eric Weisstein's World of Mathematics, Minimal Edge Cover
Eric Weisstein's World of Mathematics, Wheel Graph
Index entries for linear recurrences with constant coefficients, signature (1, 3, 1, -5, -5, 0, 4, 3, 1).
FORMULA
From Andrew Howroyd, Aug 04 2017: (Start)
a(n) = a(n-1)+3*a(n-2)+a(n-3)-5*a(n-4)-5*a(n-5)+4*a(n-7)+3*a(n-8)+a(n-9) for n>10.
G.f.: x^2*(1 + x)*(1 + 3*x - 4*x^2 - 2*x^3 - 5*x^4 - 2*x^5 - x^6)/((1 - x^2 - x^3)^2*(1 - x - x^2 - x^3)).
(End)
MATHEMATICA
LinearRecurrence[{1, 5, 7, 17, 31, 52, 99, 169, 301}, {1, 3, 1, -5, -5, 0, 4, 3, 1}, 20]
CoefficientList[Series[(-1 - 4 x + x^2 + 6 x^3 + 7 x^4 + 7 x^5 + 3 x^6 + x^7)/((-1 + x^2 + x^3)^2 (-1 + x + x^2 + x^3)), {x, 0, 20}], x]
Table[RootSum[-1 - # - #^2 + #^3 &, #^n &] - RootSum[-1 - # + #^3 &, -#^(1 + n) + #^(3 + n) &] + n RootSum[-1 - # + #^3 &, -#^(n + 1) - 8 #^(n + 2) + 13 #^(n + 3) &]/23, {n, 20}]
PROG
(PARI) Vec((1 + x)*(1 + 3*x - 4*x^2 - 2*x^3 - 5*x^4 - 2*x^5 - x^6)/((1 - x^2 - x^3)^2*(1 - x - x^2 - x^3))+O(x^40)) \\ Andrew Howroyd, Aug 04 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 03 2017
EXTENSIONS
a(2)-a(3) and terms a(14) and beyond from Andrew Howroyd, Aug 04 2017
STATUS
approved