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%I #14 Sep 08 2022 08:45:31
%S 0,2,-3,6,-8,12,-15,20,-24,30,-35,42,-48,56,-63,72,-80,90,-99,110,
%T -120,132,-143,156,-168,182,-195,210,-224,240,-255,272,-288,306,-323,
%U 342,-360,380,-399,420,-440,462,-483,506,-528,552,-575,600,-624,650,-675
%N a(2*n) = 1-n^2, a(2*n+1) = n*(n+1).
%C See A167683 for link to Hankel transform of A007325. Partial sum of signed version of A000096. [_Paul Barry_, Nov 09 2009]
%H Vincenzo Librandi, <a href="/A131723/b131723.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,2,1).
%F From _Paul Barry_, Nov 09 2009: (Start)
%F G.f.: x*(2+x)/((1+x)^3*(1-x)).
%F a(n) = -(-1)^n*(2*n^2+8*n+3-3*(-1)^n)/8. (End)
%F From _Wesley Ivan Hurt_, Jun 07 2016: (Start)
%F a(n) = -2*a(n-1) + 2*a(n-3) + a(n-4) for n>3.
%F a(n) = -(-1)^n*floor((n+1)*(n+3)/4).
%F a(2k) = - A005563(k), a(2k-1) = A002378(k) for k>0. (End)
%p A131723:=n->-(-1)^n*floor((n+1)*(n+3)/4): seq(A131723(n), n=0..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t Table[-(-1)^n*Floor[(n + 1)*(n + 3)/4], {n, 0, 100}] (* _Wesley Ivan Hurt_, Jun 07 2016 *)
%o (Magma) [-(-1)^n*(2*n^2+8*n+3-3*(-1)^n)/8: n in [0..50]]; // _Vincenzo Librandi_, Aug 10 2011
%Y Cf. A000096, A002378, A005563, A007325, A167683.
%K sign,easy
%O 0,2
%A _Paul Curtz_, Sep 16 2007
%E More terms from _Vincenzo Librandi_, Aug 10 2011
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