OFFSET
2,2
COMMENTS
Wheel graphs are defined for n>=4; extended to n=2 using formula. - Andrew Howroyd, Apr 15 2018
LINKS
Eric Weisstein's World of Mathematics, Total Dominating Set
Eric Weisstein's World of Mathematics, Wheel Graph
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1,0,0,-1,0,1,1,-1).
FORMULA
a(n) = A300738(n-1) + (n-1). - Andrew Howroyd, Apr 15 2018
G.f.: x^2*(1 + 3*x^2 - 3*x^3 - x^4 - x^5 - 8*x^6 - 2*x^7 + 8*x^8 + 11*x^9 - 9*x^10)/((-1 + x)^2*(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)).
MATHEMATICA
Table[n - 1 + RootSum[-1 - # + #^3 &, #^(n - 1) &] + (1 - (-1)^n) RootSum[-1 + #^2 + #^3 &, #^((n - 1)/2) &], {n, 2, 50}]
LinearRecurrence[{2, -1, 1, -1, 0, 0, -1, 0, 1, 1, -1}, {1, 2, 6, 8, 10, 15, 14, 12, 21, 35, 33}, 50]
CoefficientList[Series[(1 + 3 x^2 - 3 x^3 - x^4 - x^5 - 8 x^6 - 2 x^7 + 8 x^8 + 11 x^9 - 9 x^10)/((-1 + x)^2 (1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)), {x, 0, 50}], x]
PROG
(PARI) {my(v=concat([0, 0], Vec((3 + 4*x + 5*x^2 + 6*x^3 - 8*x^5 - 9*x^6)/((1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^50)))); vector(#v, i, v[i]+i)} \\ Andrew Howroyd, Apr 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 11 2018
EXTENSIONS
a(2)-a(3) and terms a(20) and beyond from Andrew Howroyd, Apr 15 2018
STATUS
approved