A051928 Number of independent sets of vertices in graph K_3 X C_n (n > 2).

4, 1, 13, 34, 121, 391, 1300, 4285, 14161, 46762, 154453, 510115, 1684804, 5564521, 18378373, 60699634, 200477281, 662131471, 2186871700, 7222746565, 23855111401, 78788080762, 260219353693, 859446141835, 2838557779204, 9375119479441, 30963916217533

Offset: 0

Author

Stephen G Penrice, Dec 19 1999

Keywords

• easy
• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• C. Bautista-Ramos and C. Guillen-Galvan, Fibonacci numbers of generalized Zykov sums, J. Integer Seq., 15 (2012), Article 12.7.8.
• Index entries for linear recurrences with constant coefficients, signature (2,4,1).

Crossrefs

Row 3 of A287376.

Programs

Mathematica

LinearRecurrence[{2,4,1},{4,1,13},30] (* Harvey P. Dale, Nov 20 2021 *)

PARI

Vec((4-7*x-5*x^2)/((1+x)*(1-3*x-x^2)) + O(x^30)) \\ Colin Barker, May 11 2017

Formula

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

G.f.: (4-7*x-5*x^2)/((1+x)*(1-3*x-x^2)). - Colin Barker, May 22 2012

a(n) = 2*(-1)^n + ((3-sqrt(13))/2)^n + ((3+sqrt(13))/2)^n. - Colin Barker, May 11 2017

a(n) = A006497+2*(-1)^n. - R. J. Mathar, Oct 20 2017