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%I #28 Jul 09 2023 08:33:36
%S 0,1,2,-1,6,-5,12,-11,20,-19,30,-29,42,-41,56,-55,72,-71,90,-89,110,
%T -109,132,-131,156,-155,182,-181,210,-209,240,-239,272,-271,306,-305,
%U 342,-341,380,-379,420,-419,462,-461,506,-505,552,-551,600,-599,650,-649,702,-701,756,-755,812,-811,870,-869,930,-929,992,-991,1056,-1055,1122,-1121,1190,-1189,1260,-1259,1332,-1331,1406
%N First differences of A000463.
%H Reinhard Zumkeller, <a href="/A188652/b188652.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2,2,-1,-1).
%F a(2n) = 1 - a(2n-1), a(2n+1) = 2*n + 1 - a(2n).
%F a(n) = A000463(n+1) - A000463(n).
%F a(2n-1) = A002378(n-1), a(2n) = - A165900(n).
%F G.f.: -x^2*(-1-3*x+x^2+x^3) / ( (x-1)^2*(1+x)^3 ). - R. J. Mathar, Apr 14 2011
%F a(n) = (2*n+3-(2*n^2-2*n-5)*(-1)^n)/8. - _Luce ETIENNE_, Dec 18 2014
%F E.g.f.: ((4 + x - x^2)*cosh(x) - (1 - x - x^2)*sinh(x) - 4)/4. - _Stefano Spezia_, Jul 08 2023
%t Differences[Flatten[Array[{#,#^2}&,40]]] (* _Harvey P. Dale_, Aug 04 2012 *)
%o (Haskell)
%o a188652 n = a188652_list !! (n-1)
%o a188652_list = zipWith (-) (tail a000463_list) a000463_list
%Y Cf. A188653 (first differences).
%Y Cf. A000463, A002378, A165900.
%K sign,easy
%O 1,3
%A _Reinhard Zumkeller_, Apr 13 2011
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