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 A110613 #8 Sep 01 2017 03:05:23
%S A110613 1,0,3,7,29,107,421,1659,6597,26299,105029,419771,1678405,6712251,
%T A110613 26846277,107379643,429507653,1718008763,6871991365,27487878075,
%U A110613 109951337541,439805000635,1759219303493,7036875815867,28147500467269
%N A110613 a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 0, a(2) = 3.
%C A110613 A Jacobsthal related sequence (A001045). This sequence was calculated using the same rules given for A108618; the "initial seed" is the floretion given in the program code, below.
%H A110613 G. C. Greubel, <a href="/A110613/b110613.txt">Table of n, a(n) for n = 0..1000</a>
%H A110613 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-2,-8).
%F A110613 G.f.: (1-5*x+5*x^2)/((4*x-1)*(2*x-1)*(x+1)).
%F A110613 Program "Superseeker" finds:
%F A110613 a(n) + a(n+1) = A007582(n) = A007581(n+1) - A007581(n).
%F A110613 a(n+2) - a(n) = A049775(n).
%F A110613 a(n) + 2*a(n+1) + a(n+2) = A087440(n+1).
%p A110613 seriestolist(series((1-5*x+5*x^2)/((4*x-1)*(2*x-1)*(x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2tessumseq[(.5'i - .5'k - .5i' + .5k' - .5'ij' - .5'ji' - .5'jk' - .5'kj')('i + j' + 'ij' + 'ji')] Sumtype is set to:sum[Y[15]] = sum(*) (from 3rd term, disregarding signs)
%t A110613 LinearRecurrence[{5, -2, -8}, {1, 0, 3}, 50] (* _G. C. Greubel_, Sep 01 2017 *)
%o A110613 (PARI) x='x+O('x^50); Vec((1-5*x+5*x^2)/((4*x-1)*(2*x-1)*(x+1))) \\ _G. C. Greubel_, Sep 01 2017
%Y A110613 Cf. A001045, A007582, A007581, A049775, A087440, A108618, A110614.
%K A110613 easy,nonn
%O A110613 0,3
%A A110613 _Creighton Dement_, Jul 31 2005