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 A219977 #37 Sep 08 2022 08:46:04
%S A219977 1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,
%T A219977 0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,
%U A219977 -1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,-1,0,0
%N A219977 Expansion of 1/(1+x+x^2+x^3).
%H A219977 G. C. Greubel, <a href="/A219977/b219977.txt">Table of n, a(n) for n = 0..5000</a>
%H A219977 Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani, <a href="http://arxiv.org/abs/1601.07723">Non-overlapping matrices</a>, arXiv:1601.07723 [cs.DM], 2016.
%H A219977 Stefano Bilotta, <a href="http://arxiv.org/abs/1605.03785">Variable-length Non-overlapping Codes</a>, arXiv preprint arXiv:1605.03785, 2016
%H A219977 Kyu-Hwan Lee, Se-jin Oh, <a href="http://arxiv.org/abs/1601.06685">Catalan triangle numbers and binomial coefficients</a>, arXiv:1601.06685 [math.CO], 2016.
%H A219977 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1).
%F A219977 G.f.: 1/(1 +x +x^2 +x^3).
%F A219977 Euler transform of length 4 sequence [ -1, 0, 0, 1]. - _Michael Somos_, Dec 12 2012
%F A219977 a(n) = a(n+4) = -a(1-n). |a(n)| = A133872(n). REVERT transform is A036765. INVERT transform is A077962. - _Michael Somos_, Dec 12 2012
%F A219977 A038505(n+2) = p(-1) where p(x) is the unique degree-n polynomial such that p(k) = a(k) for k = 0, 1, ..., n. - _Michael Somos_, Dec 12 2012
%F A219977 From _Wesley Ivan Hurt_, Apr 22 2015: (Start)
%F A219977 a(n) +a(n-1) +a(n-2) +a(n-3) = 0.
%F A219977 a(n) = (-1)^n/2 +(-1)^(n/2 +1/4 -(-1)^n/4)/2. (End)
%e A219977 G.f. = 1 - x + x^4 - x^5 + x^8 - x^9 + x^12 - x^13 + x^16 - x^17 + x^20 - x^21 + ...
%t A219977 CoefficientList[Series[1/(1+x+x^2+x^3),{x,0,80}],x] (* or *) PadRight[{},120,{1,-1,0,0}]
%t A219977 LinearRecurrence[{-1,-1,-1},{1,-1,0},80] (* _Harvey P. Dale_, May 22 2021 *)
%o A219977 (PARI) {a(n) = [1, -1, 0, 0][n%4 + 1]} /* _Michael Somos_, Dec 12 2012 */
%o A219977 (PARI) Vec(1/(1+x+x^2+x^3) + O(x^100)) \\ _Michel Marcus_, Jan 28 2016
%o A219977 (Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1+x+x^2+x^3))); // _Vincenzo Librandi_, Apr 22 2015
%Y A219977 Cf. A036765, A038505, A049347, A077962, A133872.
%K A219977 sign,easy
%O A219977 0,1
%A A219977 _Harvey P. Dale_, Dec 02 2012