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A181900 a(n) = n * A022998(n).

%I A181900 #35 Aug 01 2022 15:25:42
%S A181900 0,1,8,9,32,25,72,49,128,81,200,121,288,169,392,225,512,289,648,361,
%T A181900 800,441,968,529,1152,625,1352,729,1568,841,1800,961,2048,1089,2312,
%U A181900 1225,2592,1369,2888,1521,3200,1681,3528,1849,3872,2025,4232,2209,4608,2401
%N A181900 a(n) = n * A022998(n).
%C A181900 Multiplicative because A022998 is. - _Andrew Howroyd_, Jul 26 2018
%H A181900 Reinhard Zumkeller, <a href="/A181900/b181900.txt">Table of n, a(n) for n = 0..10000</a>
%H A181900 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A181900 a(2*n) = 8*n^2 = A139098(n).
%F A181900 a(2*n+1) = 1 + 4*n + 4*n^2 = A016754(n).
%F A181900 From _Colin Barker_, Apr 01 2012: (Start)
%F A181900 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
%F A181900 G.f.: x*(1+8*x+6*x^2+8*x^3+x^4)/((1-x)^3*(1+x)^3). (End)
%F A181900 a(n) = numerator(2*n^2/(n^2+1)). - _Vincenzo Librandi_, Aug 19 2014
%F A181900 From _Amiram Eldar_, Feb 22 2022: (Start)
%F A181900 Sum_{n>=1} 1/a(n) = 7*Pi^2/48.
%F A181900 Sum_{n>=1} (-1)^(n+1)/a(n) = 5*Pi^2/48. (End)
%F A181900 From _G. C. Greubel_, Aug 01 2022: (Start)
%F A181900 a(n) = n^2*(3 + (-1)^n)/2.
%F A181900 E.g.f.: (1/2)*x*(-1 + x + 3*(1 + x)*exp(2*x)). (End)
%t A181900 LinearRecurrence[{0,3,0,-3,0,1},{0,1,8,9,32,25},50] (* _Harvey P. Dale_, Dec 01 2018 *)
%o A181900 (Haskell)
%o A181900 a181900 n = a022998 n * n
%o A181900 (PARI) a(n)=if(n%2,n^2,2*n^2) \\ _Charles R Greathouse IV_, Aug 07 2012
%o A181900 (Magma) [Numerator(2*n^2/(n^2+1)): n in [0..50]]; // _Vincenzo Librandi_, Aug 19 2014
%o A181900 (SageMath) [n^2*(1 + ((n+1)%2)) for n in (0..60)] # _G. C. Greubel_, Aug 01 2022
%Y A181900 Cf. A016754, A022998, A086500 (partial sums), A139098.
%K A181900 nonn,easy,mult
%O A181900 0,3
%A A181900 _Reinhard Zumkeller_, Mar 31 2012