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 A276283 #15 Mar 27 2019 10:00:06
%S A276283 1,3,7,11,13,15,19,23,25,27,31,35,37,39,43,47,49,51,55,59,61,63,67,71,
%T A276283 73,75,79,83,85,87,91,95,97,99,103,107,109,111,115,119,121,123,127,
%U A276283 131,133,135,139,143,145,147,151,155,157,159,163,167,169,171,175,179,181,183,187,191,193,195,199,203,205,207,211
%N A276283 Expansion of (1 + x + 3*x^2 + x^3)/((1 - x)^2*(1 + x^2)).
%C A276283 Primes in this sequence: 3, 7, 11, 13, 19, 23, 31, 37, 43, 47, 59, 61, 67, 71, 73, 79, 83, 97, 103, 107, 109, 127, 131, 139, 151, 157, 163, 167, 179, 181, 191, 193, 199, ... (A040116, offset 2).
%H A276283 Carauleanu Marc, <a href="/A276283/b276283.txt">Table of n, a(n) for n = 0..4444</a>
%H A276283 Ilya Gutkovskiy, <a href="/A276283/a276283.jpg">Illustration</a>
%H A276283 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1)
%F A276283 O.g.f.: (1 + x + 3*x^2 + x^3)/((1 - x)^2*(1 + x^2)).
%F A276283 E.g.f.: (1 + 3*x)*exp(x) - sin(x).
%F A276283 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4).
%F A276283 a(n) = 3*n - sin(Pi*n/2) + 1.
%F A276283 a(n) = (6*n - i*((-i)^n - i^n + 2*i))/2, where i is the imaginary unit.
%p A276283 a:=series((1+x+3*x^2+x^3)/((1-x)^2*(1+x^2)),x=0,71): seq(coeff(a,x,n),n=0..70); # _Paolo P. Lava_, Mar 27 2019
%t A276283 LinearRecurrence[{2, -2, 2, -1}, {1, 3, 7, 11}, 71]
%t A276283 Table[3 n - Sin[Pi (n/2)] + 1, {n, 0, 70}]
%t A276283 Table[(6 n - I ((-I)^n - I^n + 2 I))/2, {n, 0, 70}]
%o A276283 (PARI) Vec((1+x+3*x^2+x^3)/((1-x)^2*(1+x^2)) + O(x^99)) \\ _Altug Alkan_, Aug 27 2016
%Y A276283 Cf. A005408, A040116.
%K A276283 nonn,easy
%O A276283 0,2
%A A276283 _Ilya Gutkovskiy_, Aug 27 2016