A051931 Number of independent sets of nodes in graph K_6 X C_n (n > 2).

7, 1, 43, 229, 1447, 8881, 54763, 337429, 2079367, 12813601, 78961003, 486579589, 2998438567, 18477210961, 113861704363, 701647437109, 4323746327047, 26644125399361, 164188498723243, 1011775117738789, 6234839205156007, 38420810348674801, 236759701297204843

Offset: 0

Author

Stephen G Penrice, Dec 19 1999

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,7,1).

Crossrefs

Row 6 of A287376.

Programs

Magma

I:=[7, 1, 43]; [n le 3 select I[n] else 5*Self(n-1)+7*Self(n-2)+Self(n-3): n in [1..25]]; // Vincenzo Librandi, Apr 27 2012

Mathematica

CoefficientList[Series[(7-34*x-11*x^2)/((1+x)*(1-6*x-x^2)),{x,0,30}],x] (* Vincenzo Librandi, Apr 27 2012 *)

PARI

Vec((7 - 34*x - 11*x^2) / ((1 + x)*(1 - 6*x - x^2)) + O(x^40)) \\ Colin Barker, Nov 24 2017

Formula

a(n) = 5*a(n-1) + 7*a(n-2) + a(n-3).

G.f.: (7 - 34*x - 11*x^2) / ((1 + x)*(1 - 6*x - x^2)). - Colin Barker, Apr 18 2012

From Colin Barker, Nov 24 2017: (Start)

a(n) = (3 - sqrt(10))^n + (3 + sqrt(10))^n + 5 for n even.

a(n) = (3 - sqrt(10))^n + (3 + sqrt(10))^n - 5 for n odd.

(End)

Extensions

More terms from James Sellers, Dec 20 1999