A258160 a(n) = 8*Lucas(n).

16, 8, 24, 32, 56, 88, 144, 232, 376, 608, 984, 1592, 2576, 4168, 6744, 10912, 17656, 28568, 46224, 74792, 121016, 195808, 316824, 512632, 829456, 1342088, 2171544, 3513632, 5685176, 9198808, 14883984, 24082792, 38966776, 63049568, 102016344, 165065912

Offset: 0

Author

Bruno Berselli, May 22 2015

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..300
• Tanya Khovanova, Recursive Sequences: a(n) = a(n-1)+a(n-2).
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A022112, A039834, A156279.

Cf. A022091: 8*Fibonacci(n).

Cf. A022352: Fibonacci(n+6) + Fibonacci(n-6).

Cf. sequences with the formula Fibonacci(n+k)-Fibonacci(n-k): A000045 (k=1); A000032 (k=2); A022087 (k=3); A022379 (k=4, without initial 6); A022345 (k=5); this sequence (k=6); A022363 (k=7).

Programs

Magma

[8*Lucas(n): n in [0..40]];

Mathematica

Table[8 LucasL[n], {n, 0, 40}]
CoefficientList[Series[8*(2 - x)/(1 - x - x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 21 2017 *)

PARI

a(n)=([0,1; 1,1]^n*[16;8])[1,1] \\ Charles R Greathouse IV, Oct 07 2015

Sage

[8*lucas_number2(n, 1, -1) for n in (0..40)]

Formula

G.f.: 8*(2 - x)/(1 - x - x^2).

a(n) = Fibonacci(n+6) - Fibonacci(n-6), where Fibonacci(-6..-1) = -8, 5, -3, 2, -1, 1 (see similar sequences listed in Crossrefs).

a(n) = Lucas(n+4) + Lucas(n) + Lucas(n-4), where Lucas(-4..-1) = 7, -4, 3, -1.

a(n) = a(n-1) + a(n-2) for n>1, a(0)=16, a(1)=8.

a(n) = 2*A156279(n).

a(n+1) = 4*A022112(n).