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 A301695 #20 Aug 30 2023 17:00:18
%S A301695 1,7,17,33,55,81,113,151,193,241,295,353,417,487,561,641,727,817,913,
%T A301695 1015,1121,1233,1351,1473,1601,1735,1873,2017,2167,2321,2481,2647,
%U A301695 2817,2993,3175,3361,3553,3751,3953,4161,4375,4593,4817,5047,5281,5521,5767,6017,6273
%N A301695 Expansion of (1 + 5*x + 4*x^2 + 5*x^3 + x^4)/((1 - x)^2*(1 - x^3)).
%H A301695 Ray Chandler, <a href="/A301695/b301695.txt">Table of n, a(n) for n = 0..1000</a>
%H A301695 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A301695 G.f.: (1 + 5*x + 4*x^2 + 5*x^3 + x^4)/((1 - x)^2*(1 - x^3)).
%F A301695 a(n) = (8*n*(n + 1) - 2*((n - 1)^2 mod 3) + 5)/3. Therefore: a(3*k + r) = 8*k*(3*k + 2*r + 1) + 8*r + (-1)^r. Example: a(13) = a(3*4+1) = 8*4*(3*4 + 2*1 + 1) + 8*1 + (-1)^1 = 487. - _Bruno Berselli_, Mar 26 2018
%t A301695 Table[(8 n (n + 1) - 2 ((n-1)^2 mod 3) + 5)/3, {n, 0, 40}] (* _Bruno Berselli_, Mar 26 2018 *)
%o A301695 (Magma) [(8*n*(n+1)-2*((n-1)^2 mod 3)+5)/3: n in [0..50]]; // _Bruno Berselli_, Mar 26 2018
%o A301695 (PARI) Vec((1 + 5*x + 4*x^2 + 5*x^3 + x^4)/((1 - x)^2*(1 - x^3)) + O(x^50)) \\ _Felix Fröhlich_, Mar 26 2018
%Y A301695 Partial sums of A301694.
%K A301695 nonn,easy
%O A301695 0,2
%A A301695 _N. J. A. Sloane_, Mar 25 2018