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 A219721 #32 Feb 24 2023 03:09:44
%S A219721 1,8,13,20,22,29,34,41,43,50,55,62,64,71,76,83,85,92,97,104,106,113,
%T A219721 118,125,127,134,139,146,148,155,160,167,169,176,181,188,190,197,202,
%U A219721 209,211,218,223,230,232,239,244,251,253,260,265,272,274,281,286,293
%N A219721 Expansion of (1+7*x+5*x^2+7*x^3+x^4)/(1-x-x^4+x^5).
%C A219721 Positive values of y in the Diophantine equation 21*x+1 = y^2; the corresponding values of x are given in A219391.
%C A219721 Equivalently, numbers that are congruent to {1,8,13,20} mod 21.
%C A219721 The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4 etc.
%H A219721 Bruno Berselli, <a href="/A219721/b219721.txt">Table of n, a(n) for n = 0..1000</a>
%H A219721 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A219721 G.f.: (1+7*x+5*x^2+7*x^3+x^4)/((1+x)*(1-x)^2*(1+x^2)).
%F A219721 a(n) = -a(-n-1) = (42*n-6*i^(n*(n-1))-7*(-1)^n+5)/8 +2, where i=sqrt(-1).
%t A219721 CoefficientList[Series[(1 + 7 x + 5 x^2 + 7 x^3 + x^4)/(1 - x - x^4 + x^5), {x, 0, 60}], x]
%t A219721 LinearRecurrence[{1, 0, 0, 1, -1}, {1, 8, 13, 20, 22}, 60] (* _Vincenzo Librandi_, Aug 18 2013 *)
%o A219721 (PARI) Vec((1+7*x+5*x^2+7*x^3+x^4)/(1-x-x^4+x^5)+O(x^60))
%o A219721 (Maxima) makelist(coeff(taylor((1+7*x+5*x^2+7*x^3+x^4)/(1-x-x^4+x^5), x, 0, n), x, n), n, 0, 60);
%o A219721 (Magma) I:=[1,8,13,20,22]; [n le 5 select I[n] else Self(n-1) +Self(n-4)-Self(n-5): n in [1..60]]; // _Vincenzo Librandi_, Aug 18 2013
%Y A219721 Cf. A219391.
%K A219721 nonn,easy
%O A219721 0,2
%A A219721 _Bruno Berselli_, Nov 26 2012