A297047 Number of edge covers in the n-wheel graph.

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

Robert Israel, Table of n, a(n) for n = 1..1811

Eric Weisstein's World of Mathematics, Edge Cover

Eric Weisstein's World of Mathematics, Wheel Graph

Index entries for linear recurrences with constant coefficients, signature (4, 0, -5, -2).

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

Adjacent sequences: A297044 A297045 A297046 * A297048 A297049 A297050

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 24 2017

Status

approved