A051930 Number of independent sets of vertices in graph K_5 X C_n (n > 2).

6, 1, 31, 136, 731, 3771, 19606, 101781, 528531, 2744416, 14250631, 73997551, 384238406, 1995189561, 10360186231, 53796120696, 279340789731, 1450500069331, 7531841136406, 39109705751341, 203080369893131, 1054511555216976, 5475638145978031, 28432702285107111

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 (4,6,1).

Crossrefs

Row 5 of A287376.

Programs

Magma

I:=[6, 1, 31]; [n le 3 select I[n] else 4*Self(n-1)+6*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2012

Mathematica

LinearRecurrence[{4,6,1},{6,1,31},30] (* Vincenzo Librandi, Jun 17 2012 *)

PARI

Vec((6 - 23*x - 9*x^2) / ((1 + x)*(1 - 5*x - x^2)) + O(x^40)) \\ Colin Barker, Nov 24 2017

Formula

a(n) = 4*a(n-1) + 6*a(n-2) + a(n-3).

G.f.: (6 - 23*x - 9*x^2) / ((1 + x)*(1 - 5*x - x^2)). - Colin Barker, May 22 2012

From Colin Barker, Nov 24 2017: (Start)

a(n) = ((5-sqrt(29))/2)^n + ((5+sqrt(29))/2)^n + 4 for n even.

a(n) = ((5-sqrt(29))/2)^n + ((5+sqrt(29))/2)^n - 4 for n odd.

(End)

Extensions

More terms from James Sellers, Dec 20 1999