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 A330133 #15 Sep 08 2022 08:46:24
%S A330133 0,1,3,6,10,16,23,31,40,51,63,76,90,106,123,141,160,181,203,226,250,
%T A330133 276,303,331,360,391,423,456,490,526,563,601,640,681,723,766,810,856,
%U A330133 903,951,1000,1051,1103,1156,1210,1266,1323,1381,1440,1501,1563,1626,1690,1756
%N A330133 a(n) = (1/16)*(5 + (-1)^(1+n) - 4*cos(n*Pi/2) + 10*n^2).
%C A330133 For n > 0, partial sums of A047201.
%H A330133 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).
%F A330133 O.g.f.: -x*(1 + x + x^2 + x^3 + x^4)/((-1 + x)^3*(1 + x)*(1 + x^2)).
%F A330133 E.g.f.: (1/16)*(-exp(-x) + 5*exp(x)*(1 + 2*x + x^2) - 4*cos(x)).
%F A330133 a(n) = 2*a(n-1) - a(n-2) + a(n-4) -2*a(n-5) + a(n-6) for n > 5.
%F A330133 a(2*n-1) = A005891(n-1) for n > 0.
%F A330133 a(4*n) = 10*n^2. - _Bernard Schott_, Dec 06 2019
%p A330133 gf:=(1/16)*(-exp(-x) + 5*exp(x)*(1 + 2*x + 2*x^2) - 4*cos(x)); ser := series(gf, x, 54):
%p A330133 seq(factorial(n)*coeff(ser, x, n), n = 0 .. 53)
%t A330133 Table[(1/16)*(5+(-1)^(1+n)-4*Cos[n*Pi/2]+10*n^2),{n,0,53}]
%t A330133 LinearRecurrence[{2,-1,0,1,-2,1},{0,1,3,6,10,16},60] (* _Harvey P. Dale_, Jul 21 2021 *)
%o A330133 (Magma) I:=[0, 1, 3, 6, 10, 16]; [n le 6 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-4)-2*Self(n-5)+Self(n-6): n in [1..54]];
%o A330133 (PARI) concat([0], Vec(-x*(1 + x + x^2 + x^3 + x^4)/((-1 + x)^3*(1 + x)*(1 + x^2))+O(x^54)))
%Y A330133 Cf. A005891, A033583 (10*n^2), A047201.
%K A330133 easy,nonn
%O A330133 0,3
%A A330133 _Stefano Spezia_, Dec 02 2019