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%I #40 Sep 08 2022 08:45:53
%S 1,2,1,8,1,18,1,32,1,50,1,72,1,98,1,128,1,162,1,200,1,242,1,288,1,338,
%T 1,392,1,450,1,512,1,578,1,648,1,722,1,800,1,882,1,968,1,1058,1,1152,
%U 1,1250,1,1352,1,1458,1,1568,1,1682,1,1800,1,1922,1,2048,1,2178
%N a(2*k-1)=1, a(2*k)=2*k^2 (definition by T. M. Apostol, see References).
%D T. M. Apostol, Calculus, Volume 1, John Wiley & Sons, 1967 (2nd ed.), p. 378-379.
%H Bruno Berselli, <a href="/A176889/b176889.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F G.f.: x*(1 + 2*x - 2*x^2 + 2*x^3 + x^4)/(1-x^2)^3.
%F a(n) = a(-n) = 1+((-1)^n+1)*(n^2-2)/4.
%t CoefficientList[Series[(1 + 2 x - 2 x^2 + 2 x^3 + x^4) / (1 - x^2)^3, {x, 0, 65}], x] (* _Vincenzo Librandi_, Aug 19 2013 *)
%o (Magma) &cat[[1, 2*n^2]: n in [1..33]];
%o (Magma) [1+((-1)^n+1)*(n^2-2)/4: n in [1..70]]; // _Vincenzo Librandi_, Aug 19 2013
%K nonn,easy
%O 1,2
%A _Bruno Berselli_, Jan 11 2011
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