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 (5,-5,-5,5,-1).
FORMULA
G.f.: (1 +5*x -16*x^2 +7*x^3 +2*x^4)/((1+x)*(1-3*x+x^2)^2). - Colin Barker, Nov 25 2014
a(n) = (n+1)*Lucas(2*n) + 3*Fibonacci(2*n) - (-1)^n. - G. C. Greubel, Oct 01 2019
MAPLE
f:= combinat[fibonacci]: seq((n+1)*(f(2*n+1) + f(2*n-1)) + 3*f(2*n) -(-1)^n, n=0..40); # G. C. Greubel, Oct 01 2019
MATHEMATICA
Table[(n+1)*LucasL[2*n] +3*Fibonacci[2*n] -(-1)^n, {n, 0, 40}] (* G. C. Greubel, Oct 01 2019 *)
PROG
(PARI) vector(41, n, f=fibonacci; n*(f(2*n-1) + f(2*n-3)) + 3*f(2*n-2) +(-1)^n) \\ G. C. Greubel, Oct 01 2019
(Magma) [(n+1)*Lucas(2*n) + 3*Fibonacci(2*n) -(-1)^n: n in [0..40]]; // G. C. Greubel, Oct 01 2019
(Sage) [(n+1)*lucas_number2(2*n, 1, -1) + 3*fibonacci(2*n) -(-1)^n for n in (0..40)] # G. C. Greubel, Oct 01 2019
(GAP) List([0..40], n-> (n+1)*Lucas(1, -1, 2*n)[2] + 3*Fibonacci(2*n) -(-1)^n ); # G. C. Greubel, Oct 01 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved