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%I #18 Sep 08 2022 08:45:30
%S 0,0,1,0,-1,1,0,2,-4,4,-3,6,-9,9,-8,12,-16,16,-15,20,-25,25,-24,30,
%T -36,36,-35,42,-49,49,-48,56,-64,64,-63,72,-81,81,-80,90,-100,100,-99,
%U 110,-121,121,-120,132,-144,144,-143,156,-169,169,-168
%N a(4n) = -n^2, a(4n+1) = n^2, a(4n+2) = 1-n^2, a(4n+3) = n*(n+1).
%C Up to signs, the first differences are in A131804. - _R. J. Mathar_, Mar 17 2009
%H Vincenzo Librandi, <a href="/A131118/b131118.txt">Table of n, a(n) for n = 0..1000</a>
%F From _R. J. Mathar_, Mar 17 2009: (Start)
%F a(n) = -2*a(n-1) -2*a(n-2) -2*a(n-3) +2*a(n-5) +2*a(n-6) +2*a(n-7) +a(n-8).
%F G.f.: x^2*(1+x^2+x^3+2*x)/((1-x)*(1+x^2)^2*(1+x)^3). (End)
%F a(n) = ((-2*n^2+4*n+7)*(-1)^n - 2*((n+4)+(n+2)*(-1)^n)*i^(n*(n+1))+5)/32, where i=sqrt(-1). - _Bruno Berselli_, Mar 27 2012
%p seq(((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1,2) +5)/32, n=0..60); # _G. C. Greubel_, Nov 18 2019
%t Table[((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial[n+1,2] +5)/32, {n,0,60}] (* _G. C. Greubel_, Nov 18 2019 *)
%o (PARI) a(n) = ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1,2) +5)/32; \\ _G. C. Greubel_, Nov 18 2019
%o (Magma) [((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1,2) +5)/32: n in [0..60]]; // _G. C. Greubel_, Nov 18 2019
%o (Sage) [((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1,2) +5)/32 for n in (0..60)] # _G. C. Greubel_, Nov 18 2019
%o (GAP) List([0..60], n-> ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1,2) +5)/32 ); # _G. C. Greubel_, Nov 18 2019
%K sign,easy
%O 0,8
%A _Paul Curtz_, Sep 24 2007
%E More terms from _Sean A. Irvine_, Mar 13 2011