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 A106249 #50 Jan 24 2021 10:41:21
%S A106249 1,0,1,2,3,2,3,4,5,4,5,6,7,6,7,8,9,8,9,10,11,10,11,12,13,12,13,14,15,
%T A106249 14,15,16,17,16,17,18,19,18,19,20,21,20,21,22,23,22,23,24,25,24,25,26,
%U A106249 27,26,27,28,29,28,29,30,31,30,31,32,33,32,33,34,35,34,35,36,37,36,37,38
%N A106249 Expansion of (1-x+x^2+x^3)/(1-x-x^4+x^5).
%C A106249 Conjecture: number of roots of x^n + 1 in the left half-plane for n > 0. - _Michel Lagneau_, Oct 31 2012
%C A106249 Maximum bias of polyominoes with n+1 squares. Define the bias of a polyomino to be the difference between the number of black squares and the number of white squares when chessboard coloring is applied to the polyomino. Maximum bias for the value n is defined to be the maximum value of bias among all polyominoes of n squares. - _John Mason_, Dec 24 2013
%H A106249 Vincenzo Librandi, <a href="/A106249/b106249.txt">Table of n, a(n) for n = 0..1000</a>
%H A106249 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A106249 G.f.: (1-x+x^2+x^3)/(1-x-x^4+x^5)=(1+x^2+2x^3+x^4+2x^5+x^6)/(1-x^4)^2.
%F A106249 a(n) = sum{k=0..n, -mu(k mod 4)}.
%F A106249 a(n) = cos(Pi*n/2)/2-sin(Pi*n/2)/2+(-1)^n/4+(2n+1)/4.
%F A106249 a(n) = sum{k=0..n, Jacobi(2^k, 2k+1)} [Conjecture]. - _Paul Barry_, Jul 23 2005
%F A106249 a(n) = sum{k=0..n, Product{j=1..k, ((-1)^j)^(k-j+1)}}. - _Paul Barry_, Nov 09 2007
%F A106249 a(n) = A083219(n-1). - _R. J. Mathar_, Aug 28 2008
%F A106249 a(n) = numbers of times cos(-Pi/n+2k*Pi/n) < 0 for k = 0..n-1. - _Michel Lagneau_, Nov 02 2012
%F A106249 a(n) = ((n - 1) mod 4)/2 + (n+1)/2 - 1. - _John Mason_, Dec 24 2013
%F A106249 a(n) = A018837(n-1) for n > 2. - _Georg Fischer_, Oct 07 2018
%p A106249 a:= n-> n-1 - 2*floor((n-1)/4):
%p A106249 seq(a(n), n=0..75); # _Alois P. Heinz_, Jan 24 2021
%t A106249 CoefficientList[Series[(1 - x + x^2 + x^3)/(1 - x - x^4 + x^5), {x, 0, 100}], x] (* _Vincenzo Librandi_, Dec 31 2013 *)
%t A106249 LinearRecurrence[{1,0,0,1,-1},{1,0,1,2,3},80] (* _Harvey P. Dale_, May 07 2018 *)
%o A106249 (PARI) a(n)=([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; -1,1,0,0,1]^n*[1;0;1;2;3])[1,1] \\ _Charles R Greathouse IV_, Sep 02 2015
%o A106249 (GAP) List([0..80],n->((n-1) mod 4)/2+(n+1)/2-1); # _Muniru A Asiru_, Oct 07 2018
%Y A106249 Cf. A008611.
%K A106249 easy,nonn
%O A106249 0,4
%A A106249 _Paul Barry_, Apr 27 2005
%E A106249 _John Mason_'s contributions corrected for offset by _Eric M. Schmidt_, Dec 30 2013