OFFSET
0,1
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Mark W. Coffey, James L. Hindmarsh, Matthew C. Lettington, John Pryce, On Higher Dimensional Interlacing Fibonacci Sequences, Continued Fractions and Chebyshev Polynomials, arXiv:1502.03085 [math.NT], 2015 (see p. 31).
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (3,-1).
FORMULA
a(n-1) = 4*Fibonacci(2*n) + Fibonacci(2*n-1) + Fibonacci(2*n+1).
a(n) + a(n+1) = A055849(n+2).
a(n) = 3*a(n-1) - a(n-2) with a(0)=7 and a(1)=19. - Philippe Deléham, Nov 16 2008
a(n) = (2^(-1-n)*((3-sqrt(5))^n*(-17+7*sqrt(5)) + (3+sqrt(5))^n*(17+7*sqrt(5)))) / sqrt(5). - Colin Barker, Oct 14 2015
From G. C. Greubel, Jan 17 2020: (Start)
a(n) = Fibonacci(2*n+4) + Lucas(2*n+3).
E.g.f.: 2*exp(3*t/2)*(cosh(sqrt(5)*t/2) + (4/sqrt(5))*sinh(sqrt(5)*t/2)). (End)
MAPLE
F := proc(n) combinat[fibonacci](n) ; end: A100545 := proc(n) 4*F(2*(n+1)) + F(2*n+1)+F(2*n+3) ; end: for n from 0 to 30 do printf("%d, ", A100545(n)) ; od ; # R. J. Mathar, Oct 26 2006
MATHEMATICA
Table[Fibonacci[2*(n+2)] + LucasL[2*n+3], {n, 0, 30}] (* G. C. Greubel, Jan 17 2020 *)
PROG
(PARI) Vec((7-2*x)/(1-3*x+x^2) + O(x^30)) \\ Michel Marcus, Feb 11 2015
(Magma) [Fibonacci(2*n+4) +Lucas(2*n+3): n in [0..30]]; // G. C. Greubel, Jan 17 2020
(Sage) [fibonacci(2*n+4) +lucas_number2(2*n+3, 1, -1) for n in (0..30)] # G. C. Greubel, Jan 17 2020
(GAP) List([0..30], n-> Fibonacci(2*n+4) +Lucas(1, -1, 2*n+3)[2] ); # G. C. Greubel, Jan 17 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Dec 31 2004
EXTENSIONS
Corrected and extended by T. D. Noe and R. J. Mathar, Oct 26 2006
STATUS
approved