OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Gear Graph
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).
FORMULA
a(n) = Lucas(2*n) + n*Fibonacci(2*n) for n > 0.
G.f.: x*(4 - 11*x + 8*x^2 - 2*x^3)/(1 - 3*x + x^2)^2. - Ilya Gutkovskiy, May 23 2017
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4) for n>4. - Colin Barker, Jun 05 2017
MATHEMATICA
Table[LucasL[2 n] + n Fibonacci[2 n], {n, 20}]
LinearRecurrence[{6, -11, 6, -1}, {4, 13, 42, 131}, 30]
CoefficientList[Series[(42 - 121 x + 74 x^2 - 13 x^3)/(1 - 3 x + x^2)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Oct 02 2017 *)
PROG
(Python)
from sympy import lucas, fibonacci
def a(n): return lucas(2*n) + n*fibonacci(2*n) # Indranil Ghosh, May 24 2017
(PARI) Vec(x*(4 - 11*x + 8*x^2 - 2*x^3)/(1 - 3*x + x^2)^2 + O(x^30)) \\ Colin Barker, Jun 05 2017
(PARI) a(n) = fibonacci(2*n-1) + n*fibonacci(2*n) + fibonacci(2*n+1); \\ Altug Alkan, Oct 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 23 2017
STATUS
approved