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%I #27 Sep 08 2022 08:44:58
%S 3,137,6436,302355,14204249,667297348,31348771107,1472724944681,
%T 69186723628900,3250303285613619,152695067700211193,
%U 7173417878624312452,336997945227642474051,15831730007820571967945,743754312422339240019364,34940620953842123708942163,1641465430518157475080262297
%N a(n) = (F(8*n+6) + F(8*n+1))/3, where F = A000045 (the Fibonacci sequence).
%H Indranil Ghosh, <a href="/A049677/b049677.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)=3, a(1)=137.
%F G.f.: (3-4*x)/(1-47*x+x^2). (End)
%e a(2) = (F(8 * 2 + 6) + F(8 * 2 + 1)) / 3 = (F(22) + F(17)) / 3 = (17711 + 1597) / 3 = 19308 / 3 = 6436. - _Indranil Ghosh_, Feb 05 2017
%t Table[(Fibonacci[8*n+6] + Fibonacci[8*n+1])/3, {n,0,30}] (* or *) LinearRecurrence[{47,-1}, {3,137}, 30] (* _G. C. Greubel_, Dec 02 2017 *)
%o (PARI) a(n) = (fibonacci(8*n+6)+fibonacci(8*n+1))/3; \\ _Michel Marcus_, Feb 05 2017
%o (Magma) [(Fibonacci(8*n+6) + Fibonacci(8*n+1))/3: n in [0..30]]; // _G. C. Greubel_, Dec 02 2017
%Y Cf. A000045, A049676, A049678, A049679.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_
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