A051929 Number of independent sets of vertices in graph K_4 X C_n (n > 2).

5, 1, 21, 73, 325, 1361, 5781, 24473, 103685, 439201, 1860501, 7881193, 33385285, 141422321, 599074581, 2537720633, 10749957125, 45537549121, 192900153621, 817138163593, 3461452808005, 14662949395601, 62113250390421, 263115950957273, 1114577054219525

Offset: 0

Author

Stephen G Penrice, Dec 19 1999

Keywords

• easy
• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,5,1).

Crossrefs

Row 4 of A287376.

Programs

PARI

Vec((5 - 14*x - 7*x^2) / ((1 + x)*(1 - 4*x - x^2)) + O(x^30)) \\ Colin Barker, May 11 2017

Formula

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

From Colin Barker, May 22 2012: (Start)

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

G.f.: (5 - 14*x - 7*x^2) / ((1 + x)*(1 - 4*x - x^2)).

(End)

Extensions

More terms from James Sellers, Dec 20 1999