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 A127980 #23 May 25 2023 16:14:25
%S A127980 1,5,14,37,90,213,490,1109,2474,5461,11946,25941,55978,120149,256682,
%T A127980 546133,1157802,2446677,5155498,10835285,22719146,47535445,99265194,
%U A127980 206918997,430615210,894784853,1856678570,3847574869,7963585194
%N A127980 a(n) = (n + 2/3)*2^(n-1) - 1/2 - (-1)^(n-1)*(1/6).
%H A127980 G. C. Greubel, <a href="/A127980/b127980.txt">Table of n, a(n) for n = 1..1000</a>
%H A127980 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 A127980 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-4,4).
%F A127980 G.f.: x*(1+x-3*x^2)/((1-x)*(1+x)*(1-2*x)^2). - _Colin Barker_, Apr 02 2012
%F A127980 E.g.f.: ((1 + 3*x)*cosh(2*x) - 2*sinh(x) + cosh(x)*((2 + 6*x)*sinh(x) - 1))/3. - _Stefano Spezia_, May 25 2023
%t A127980 Table[(n+2/3)2^(n-1) - 1/2 -(-1)^(n-1)*(1/6), {n, 1, 50}]
%t A127980 LinearRecurrence[{4,-3,-4,4}, {1,5,14,37}, 50] (* _G. C. Greubel_, May 08 2018 *)
%o A127980 (PARI) x='x+O('x^30); Vec(x*(1+x-3*x^2)/((1-x)*(1+x)*(1-2*x)^2)) \\ _G. C. Greubel_, May 08 2018
%o A127980 (Magma) I:=[1,5,14,37]; [n le 4 select I[n] else 4*Self(n-1)-3*Self(n-2)-4*Self(n-3)+4*Self(n-4): n in [1..30]]; // _G. C. Greubel_, May 08 2018
%Y A127980 Cf. A073371, A127976, A127978, A127979, A073371.
%K A127980 nonn,easy
%O A127980 1,2
%A A127980 _Artur Jasinski_, Feb 09 2007