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 A127978 #32 Sep 08 2022 08:45:29
%S A127978 3,5,15,31,75,163,367,799,1747,3771,8119,17367,37019,78579,166271,
%T A127978 350735,737891,1548587,3242823,6776903,14136363,29437795,61205775,
%U A127978 127071871,263464435,545570203,1128423127,2331411639,4811954107
%N A127978 a(n) = ((15*n + 34)/54)*2^(n-1) - (-1)^(n-1)*(6*n + 5)/27.
%C A127978 In the Bosma's paper there is an error (see table of the first few values at p. 37): for n=1 ((15*n+34)/54)*2^(n-1)-(-1)^(n-1)*(6*n+5)/27 is 1/2 and not 1.
%H A127978 G. C. Greubel, <a href="/A127978/b127978.txt">Table of n, a(n) for n = 2..1000</a>
%H A127978 W. Bosma, <a href="http://dx.doi.org/10.5802/jtnb.301">Signed bits and fast exponentiation</a>, Journal de Théorie des Nombres de Bordeaux, Vol. 13, Fasc. 1 (2001), p. 38 (Proposition 7).
%H A127978 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-4,-4)
%F A127978 G.f.: x^2*(3-x-4*x^2-2*x^3)/((1+x)^2*(1-2*x)^2). - _Colin Barker_, Apr 02 2012
%t A127978 Table[((15n+34)/54)2^(n-1) -((-1)^(n-1))(6n+5)/27, {n, 2, 50}]
%t A127978 LinearRecurrence[{2,3,-4,-4}, {3, 5, 15, 31}, 50] (* _G. C. Greubel_, May 07 2018 *)
%o A127978 (PARI) x='x+O('x^30); Vec(x^2*(3-x-4*x^2-2*x^3)/((1+x)^2*(1-2*x)^2)) \\ _G. C. Greubel_, May 07 2018
%o A127978 (Magma) I:=[3, 5, 15, 31]; [n le 4 select I[n] else 2*Self(n-1) + 3*Self(n-2) -4*Self(n-3) -4*Self(n-4): n in [1..30]]; // _G. C. Greubel_, May 07 2018
%Y A127978 Cf. A073371, A127976.
%K A127978 nonn,easy
%O A127978 2,1
%A A127978 _Artur Jasinski_, Feb 09 2007
%E A127978 Offset changed from 1 to 2 (according to Bosma's Proposition 5) from _Bruno Berselli_, Apr 02 2012