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A245799
Lucas(3*n) - Fibonacci(n).
1
2, 3, 17, 74, 319, 1359, 5770, 24463, 103661, 439170, 1860443, 7881107, 33385138, 141422091, 599074201, 2537720026, 10749956135, 45537547527, 192900151034, 817138159415, 3461452801237, 14662949384658, 62113250372707, 263115950928619, 1114577054173154
OFFSET
0,1
LINKS
FORMULA
G.f.: (2 - 7*x + 6*x^2 + 5*x^3)/((1 - x - x^2)(1 - 4*x - x^2)).
MATHEMATICA
Table[LucasL[3 n] - Fibonacci[n], {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 7 x + 6 x^2 + 5 x^3)/((1 - x - x^2) (1 - 4 x - x^2)), {x, 0, 40}], x]
PROG
(Magma) [Lucas(3*n) - Fibonacci(n): n in [0..30]];
(Python)
import sympy
{print(sympy.lucas(3*n)-sympy.fibonacci(n), end=', ') for n in range(50)}
# Derek Orr, Aug 02 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 02 2014
STATUS
approved