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 A225058 #31 Sep 08 2022 08:46:04
%S A225058 -1,1,1,3,0,5,3,7,1,9,5,11,2,13,7,15,3,17,9,19,4,21,11,23,5,25,13,27,
%T A225058 6,29,15,31,7,33,17,35,8,37,19,39,9,41,21,43,10,45,23,47,11,49,25,51,
%U A225058 12,53,27,55,13,57,29,59,14,61,31,63,15,65,33,67,16,69
%N A225058 a(4*n) = n-1. a(2*n+1) = a(4*n+2) = 2*n+1.
%C A225058 Consider the family of sequences with recurrence a(n) = 2*a(n-4)-a(n-8) where a(0) and a(4) move up in steps of 1. This here is characterized by a(0)=-1, a(4)=0:
%C A225058 -2, 1, 1, 3, -1, 5, 3, 7, 0, 9, 5, 11,...
%C A225058 -1, 1, 1, 3, 0, 5, 3, 7, 1, 9, 5, 11,... = a(n)
%C A225058 0, 1, 1, 3, 1, 5, 3, 7, 2, 9, 5, 11,... = A060819
%C A225058 1, 1, 1, 3, 2, 5, 3, 7, 3, 9, 5, 11,... = b(n)
%C A225058 2, 1, 1, 3, 3, 5, 3, 7, 4, 9, 5, 11,... .
%C A225058 a(n+4)+b(n) = A145979(n).
%C A225058 a(n+4)*b(n) = A061037(n+2).
%C A225058 a(n+4)-b(n) = repeat -1, 4, 2, 4 with period of length 4.
%H A225058 Vincenzo Librandi, <a href="/A225058/b225058.txt">Table of n, a(n) for n = 0..1000</a>
%H A225058 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A225058 a(n) = 2*a(n-4) - a(n-8).
%F A225058 a(n+4) - a(n) = A176895(n).
%F A225058 G.f.: (-1+x+x^2+3*x^3+3*x^5+x^6+x^7+2*x^4)/((-1+x)^2*(1+x)^2*(x^2+1)^2). - _R. J. Mathar_, Apr 28 2013
%t A225058 a[n_] := 1/16*(11*n-(-1)^n*(5*n+4)-2*(n+4)*Re[I^n]-4); Table[a[n], {n, 0, 47}] (* _Jean-François Alcover_, Apr 30 2013 *)
%t A225058 LinearRecurrence[{0,0,0,2,0,0,0,-1},{-1,1,1,3,0,5,3,7},80] (* _Harvey P. Dale_, Jul 14 2019 *)
%o A225058 (PARI) x='x+O('x^50); Vec((-1+x+x^2+3*x^3+3*x^5+x^6+x^7+2*x^4)/((-1+x)^2*(1+x)^2*(x^2+1)^2)) \\ _G. C. Greubel_, Sep 20 2018
%o A225058 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((-1+x+x^2+3*x^3+3*x^5+x^6+x^7+2*x^4)/((-1+x)^2*(1+x)^2*(x^2+1)^2))); // _G. C. Greubel_, Sep 20 2018
%K A225058 sign,easy
%O A225058 0,4
%A A225058 _Paul Curtz_, Apr 26 2013