A258160 - OEIS

%I #44 Aug 20 2022 18:49:43

%S 16,8,24,32,56,88,144,232,376,608,984,1592,2576,4168,6744,10912,17656,

%T 28568,46224,74792,121016,195808,316824,512632,829456,1342088,2171544,

%U 3513632,5685176,9198808,14883984,24082792,38966776,63049568,102016344,165065912

%N a(n) = 8*Lucas(n).

%H Bruno Berselli, <a href="/A258160/b258160.txt">Table of n, a(n) for n = 0..300</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html#onePlusOne">Recursive Sequences: a(n) = a(n-1)+a(n-2)</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).

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

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

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

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

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

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

%t Table[8 LucasL[n], {n, 0, 40}]

%t CoefficientList[Series[8*(2 - x)/(1 - x - x^2), {x, 0, 50}], x] (* _G. C. Greubel_, Dec 21 2017 *)

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

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

%o (PARI) a(n)=([0,1; 1,1]^n*[16;8])[1,1] \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A022112, A039834, A156279.

%Y Cf. A022091: 8*Fibonacci(n).

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

%Y 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).

%K nonn,easy

%O 0,1

%A _Bruno Berselli_, May 22 2015