OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).
FORMULA
From Colin Barker, Feb 25 2015: (Start)
a(n) = 5*a(n-1) - 5*a(n-2) - 5*a(n-3) + 5*a(n-4) - a(n-5).
G.f.: (1 +5*x -13*x^2 +8*x^3)/(1-3*x+x^2)^2. (End)
a(n) = 2*(n+1)*Lucas(2*n) + Fibonacci(2*n-4). - G. C. Greubel, Oct 01 2019
MAPLE
with(combinat); f:=fibonacci; seq(2*(n+1)*(f(2*n+1) + f(2*n-1)) + f(2*n-4), n=0..40); # G. C. Greubel, Oct 01 2019
MATHEMATICA
Table[2*(n+1)*LucasL[2*n] + Fibonacci[2*n-4], {n, 0, 40}] (* G. C. Greubel, Oct 01 2019 *)
PROG
(PARI) vector(41, n, f=fibonacci; 2*n*(f(2*n-1) + f(2*n-3)) + f(2*n-6)) \\ G. C. Greubel, Oct 01 2019
(Magma) [2*(n+1)*Lucas(2*n) + Fibonacci(2*n-4): n in [0..40]]; // G. C. Greubel, Oct 01 2019
(Sage) [2*(n+1)*lucas_number2(2*n, 1, -1) + fibonacci(2*n-4) for n in (0..40)] # G. C. Greubel, Oct 01 2019
(GAP) List([0..40], n-> 2*(n+1)*Lucas(1, -1, 2*n)[2] + Fibonacci(2*n-4) ); # G. C. Greubel, Oct 01 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved