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A297047
Number of edge covers in the n-wheel graph.
3
0, 2, 10, 41, 154, 562, 2023, 7240, 25842, 92129, 328270, 1169390, 4165231, 14835316, 52837774, 188186161, 670237602, 2387090906, 8501757271, 30279468752, 107841945274, 384084812929, 1367938393414, 4871984909782, 17351831683935, 61799465142812, 220102059235510
OFFSET
1,2
COMMENTS
Extended to a(1)-a(3) using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Edge Cover
Eric Weisstein's World of Mathematics, Wheel Graph
FORMULA
a(n) = A206776(n-1) - A000032(n-1).
a(n) = 4*a(n-1) - 5*a(n-3) - 2*a(n-4).
G.f.: x^2*(2+2*x+x^2) / ( (x^2+x-1)*(2*x^2+3*x-1) ).
a(n) = 2^(-2-n)*(2*(1-sqrt(5))^n*(1+sqrt(5)) - 2*(-1+sqrt(5))*(1+sqrt(5))^n - 3*(3-sqrt(17))^n-sqrt(17)*(3-sqrt(17))^n - 3*(3+sqrt(17))^n+sqrt(17)*(3+sqrt(17))^n). - Colin Barker, Dec 28 2017
MAPLE
f:= gfun:-rectoproc({a(n) = 4*a(n-1) - 5*a(n-3) - 2*a(n-4), a(1)=0, a(2)=2, a(3)=10, a(4)=41}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Dec 26 2017
MATHEMATICA
Table[I^(n - 1) 2^((n + 1)/2) ChebyshevT[n - 1, -3 I/(2 Sqrt[2])] - LucasL[n - 1, 1], {n, 20}]
LinearRecurrence[{4, 0, -5, -2}, {0, 2, 10, 41}, 20]
CoefficientList[Series[x (2 + 2 x + x^2)/(1 - 4 x + 5 x^3 + 2 x^4), {x, 0, 20}], x]
PROG
(PARI) first(n) = Vec(x^2*(2 + 2*x + x^2)/(1 - 4*x + 5*x^3 + 2*x^4) + O(x^(n+1)), -n) \\ Iain Fox, Dec 24 2017
CROSSREFS
Sequence in context: A125130 A110684 A197175 * A037561 A135512 A317328
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 24 2017
STATUS
approved