A049676 - OEIS

%I #27 Sep 08 2022 08:44:58

%S 1,41,1926,90481,4250681,199691526,9381251041,440719107401,

%T 20704416796806,972666870342481,45694638489299801,2146675342126748166,

%U 100848046441467864001,4737711507406862859881,222571592801681086550406,10456127150171604205009201

%N a(n) = (F(8*n+3) + F(8*n+1))/3, where F = A000045 (the Fibonacci sequence).

%H Indranil Ghosh, <a href="/A049676/b049676.txt">Table of n, a(n) for n = 0..596</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (47,-1).

%F From _Philippe Deléham_, Nov 18 2008: (Start)

%F a(n) = 47*a(n-1) - a(n-2), a(0)=1, a(1)=41.

%F G.f.: (1-6*x)/(1-47*x+x^2). (End)

%e a(2) = (F(8 * 2 + 3) + F(8 * 2 + 1)) / 3 = (F(19) + F(17)) / 3 = (4181 + 1597) / 3 = 5778 / 3 = 1926. - _Indranil Ghosh_, Feb 04 2017

%t Table[(Fibonacci[8*n + 3] + Fibonacci[8*n + 1])/3, {n, 0, 20}] (* _Wesley Ivan Hurt_, Feb 04 2017 *)

%t LinearRecurrence[{47,-1}, {1,41}, 30] (* _G. C. Greubel_, Dec 02 2017 *)

%o (PARI) for(n=0,30, print1((fibonacci(8*n + 3) + fibonacci(8*n + 1))/3, ", ")) \\ _G. C. Greubel_, Dec 02 2017

%o (Magma) [(Fibonacci(8*n + 3) + Fibonacci(8*n + 1))/3: n in [0..30]]; // _G. C. Greubel_, Dec 02 2017

%Y Cf. A000045.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_

%E More terms from _Indranil Ghosh_, Feb 04 2017