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 A094569 #22 Feb 15 2025 12:12:15
%S A094569 2,11,78,532,3649,25008,171410,1174859,8052606,55193380,378301057,
%T A094569 2592914016,17772097058,121811765387,834910260654,5722560059188,
%U A094569 39223010153665,268838511016464,1842646566961586,12629687457714635,86565165637040862,593326472001571396
%N A094569 Associated with alternating row sums of array in A094568.
%H A094569 Colin Barker, <a href="/A094569/b094569.txt">Table of n, a(n) for n = 0..1000</a>
%H A094569 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-1/quartkimberling01_2004.pdf">Orderings of products of Fibonacci numbers</a>, Fibonacci Quarterly, 42:1 (2004), pp. 28-35.
%H A094569 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,6,-1).
%F A094569 a(n) = F(4n+3) - a(n-1) for n >= 1, where a(0) = 2.
%F A094569 a(n) = (Fib(4n+5) + (-1)^n )/3. - _Ralf Stephan_, Dec 04 2004
%F A094569 a(n) = (-1)^n * sum((-1)^k*Fibonacci(4*k+3), k=0..n). - _Gary Detlefs_, Jan 22 2013
%F A094569 a(n) = 6*a(n-1) + 6*a(n-2) - a(n-3). - _Colin Barker_, Nov 19 2014
%F A094569 G.f.: -(x-2) / ((x+1)*(x^2-7*x+1)). - _Colin Barker_, Nov 19 2014
%e A094569 Obtain 11,78,532 from a(0)=2 and Fibonacci numbers 13,89,610: 11=13-2, 78=89-11, 532=610-78.
%t A094569 LinearRecurrence[{6,6,-1},{2,11,78},30] (* _Harvey P. Dale_, Feb 15 2025 *)
%o A094569 (PARI) Vec(-(x-2)/((x+1)*(x^2-7*x+1)) + O(x^100)) \\ _Colin Barker_, Nov 19 2014
%o A094569 (PARI) vector(30, n, n--;(fibonacci(4*n+5) + (-1)^n)/3) \\ _Michel Marcus_, Nov 19 2014
%Y A094569 Cf. A000045, A094568, A094567.
%K A094569 nonn,easy
%O A094569 0,1
%A A094569 _Clark Kimberling_, May 12 2004
%E A094569 More terms from _Colin Barker_, Nov 19 2014