cp's OEIS Frontend

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.

A272123 a(n) = Fibonacci(3n) - Fibonacci(2n).

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%I A272123 #29 Apr 24 2016 15:36:53
%S A272123 0,1,5,26,123,555,2440,10569,45381,193834,825275,3506867,14883984,
%T A272123 63124593,267596485,1134071130,4805348667,20359308187,86252640920,
%U A272123 365396207993,1547906421765,6557202405546,27777188626555,117667194149091,498449204352288
%N A272123 a(n) = Fibonacci(3n) - Fibonacci(2n).
%H A272123 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12,1,1).
%F A272123 a(n) = A014445(n) - A001906(n).
%F A272123 G.f.: -x*(3*x^2-2*x+1)/((x^2-3*x+1)*(x^2+4*x-1)). - _Alois P. Heinz_, Apr 21 2016
%F A272123 E.g.f.: (exp(-(sqrt(5)-2)*x)*(exp(2*sqrt(5)*x) + exp((sqrt(5)-1)*x/2) - exp((3*sqrt(5)-1)x/2) - 1))/sqrt(5). - _Ilya Gutkovskiy_, Apr 22 2016
%p A272123 a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>,
%p A272123          <1|1|-12|7>>^n. <<0, 1, 5, 26>>)[1, 1]:
%p A272123 seq(a(n), n=0..30);  # _Alois P. Heinz_, Apr 21 2016
%t A272123 Table[Fibonacci[3n] - Fibonacci[2n], {n, 0, 25}] (* _Robert Price_, Apr 21 2016 *)
%o A272123 (PARI) a(n) = fibonacci(3*n) - fibonacci(2*n); \\ _Michel Marcus_, Apr 21 2016
%Y A272123 Cf. A000045, A001906, A014445, A098317.
%K A272123 nonn,easy
%O A272123 0,3
%A A272123 _Peter M. Chema_, Apr 21 2016