This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049657 #15 Nov 28 2024 16:06:50
%S A049657 0,29,1393,65472,3075821,144498145,6788337024,318907342013,
%T A049657 14981856737617,703828359326016,33064951031585165,1553348870125176769,
%U A049657 72974331944851723008,3428240252537905804637,161054317537336721094961
%N A049657 a(n) = (F(8*n+3) - 2)/3, where F = A000045 (the Fibonacci sequence).
%H A049657 G. C. Greubel, <a href="/A049657/b049657.txt">Table of n, a(n) for n = 0..595</a>
%H A049657 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (48,-48,1).
%F A049657 G.f.: -x*(29+x) / ( (x-1)*(x^2-47*x+1) ).
%F A049657 Product_{n>=1} (1 - 1/a(n)) = 2*(1+1/sqrt(5))/3 = (2/3) * A344212. - _Amiram Eldar_, Nov 28 2024
%t A049657 LinearRecurrence[{48, -48, 1}, {0, 29, 1393}, 50] (* or *) Table[( Fibonacci[8*n+3] - 2)/3, {n,0,30}] (* _G. C. Greubel_, Dec 02 2017 *)
%o A049657 (PARI) for(n=0,30, print1((fibonacci(8*n+3) - 2)/3, ", ")) \\ _G. C. Greubel_, Dec 02 2017
%o A049657 (Magma) [(Fibonacci(8*n+3) - 2)/3: n in [0..30]]; // _G. C. Greubel_, Dec 02 2017
%Y A049657 Cf. A000045, A344212.
%K A049657 nonn,easy
%O A049657 0,2
%A A049657 _Clark Kimberling_
%E A049657 Description corrected by and more terms from _Michael Somos_