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 A100050 #26 Jul 18 2021 06:32:49
%S A100050 0,1,2,0,-4,-5,0,7,8,0,-10,-11,0,13,14,0,-16,-17,0,19,20,0,-22,-23,0,
%T A100050 25,26,0,-28,-29,0,31,32,0,-34,-35,0,37,38,0,-40,-41,0,43,44,0,-46,
%U A100050 -47,0,49,50,0,-52,-53,0,55,56,0,-58,-59,0,61,62,0,-64,-65,0,67,68,0,-70,-71,0,73,74,0,-76,-77,0,79,80,0,-82,-83,0,85,86,0
%N A100050 A Chebyshev transform of n.
%C A100050 A Chebyshev transform of x/(1-x)^2: if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
%H A100050 G. C. Greubel, <a href="/A100050/b100050.txt">Table of n, a(n) for n = 0..1000</a>
%H A100050 Michael Somos, <a href="http://cis.csuohio.edu/~somos/rfmc.txt">Rational Function Multiplicative Coefficients</a>
%H A100050 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,2,-1).
%F A100050 Euler transform of length 6 sequence [ 2, -3, -2, 0, 0, 2]. - _Michael Somos_, Mar 19 2011
%F A100050 a(n) is multiplicative with a(2^e) = -(-2)^e if e>0, a(3^e) = 0^e, a(p^e) = p^e if p == 1 (mod 6), a(p^e) = (-p)^e if p == 5 (mod 6). - _Michael Somos_, Mar 19 2011
%F A100050 G.f.: x*(1 - x^2)^3 *(1 - x^3)^2 / ((1 - x)^2 *(1 - x^6)^2) = x *(1 + x)^2 *(1 - x^2) / (1 + x^3)^2. - _Michael Somos_, Mar 19 2011
%F A100050 a(3*n) = 0, a(3*n + 1) = (-1)^n * (3*n + 1), a(3*n + 2) = (-1)^n * (3*n + 2). a(-n) = a(n). - _Michael Somos_, Mar 19 2011
%F A100050 G.f.: x(1-x^2)/(1-x+x^2)^2.
%F A100050 a(n) = 2*a(n-1) -3*a(n-2) +2*a(n-3) -a(n-4).
%F A100050 a(n) = n*Sum_{k=0..floor(n/2)} (-1)^k*binomial(n-k,k)*(n-2k)/(n-k).
%e A100050 x + 2*x^2 - 4*x^4 - 5*x^5 + 7*x^7 + 8*x^8 - 10*x^10 - 11*x^11 + 13*x^13 + ...
%t A100050 LinearRecurrence[{2, -3, 2, -1}, {0, 1, 2, 0},50] (* _G. C. Greubel_, Aug 08 2017 *)
%o A100050 (Sage) [lucas_number1(n,2,1)*lucas_number1(n,1,1) for n in range(0,88)] # _Zerinvary Lajos_, Jul 06 2008
%o A100050 (PARI) {a(n) = n * (-1)^(n\3) * sign( n%3)} /* _Michael Somos_, Mar 19 2011 */
%o A100050 (PARI) {a(n) = local(A, p, e); if( abs(n)<1, 0, A = factor(abs(n)); prod( k=1, matsize(A)[1], if( p=A[k,1], e=A[k,2]; if( p==2, -(-2)^e, (kronecker( -12, p) * p)^e))))} /* _Michael Somos_, Mar 19 2011 */
%Y A100050 Cf. A165202 (partial sums).
%Y A100050 Cf. A099837, A099443, A011655, A100047, A100048, A100051, A091684.
%K A100050 easy,sign,mult
%O A100050 0,3
%A A100050 _Paul Barry_, Oct 31 2004