cp's OEIS Frontend

A154615 a(n) = A022998(n)^2.

%I A154615 #25 Aug 13 2022 06:22:48
%S A154615 0,1,16,9,64,25,144,49,256,81,400,121,576,169,784,225,1024,289,1296,
%T A154615 361,1600,441,1936,529,2304,625,2704,729,3136,841,3600,961,4096,1089,
%U A154615 4624,1225,5184,1369,5776,1521,6400,1681,7056,1849,7744,2025,8464,2209,9216
%N A154615 a(n) = A022998(n)^2.
%C A154615 Multiplicative because A022998 is. - _Andrew Howroyd_, Jul 25 2018
%H A154615 G. C. Greubel, <a href="/A154615/b154615.txt">Table of n, a(n) for n = 0..5000</a>
%H A154615 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A154615 Denominators of 1/4 - 1/(2n)^2, if n>0.
%F A154615 a(2n+1) = A016754(n). a(2n) = 16*A000290(n).
%F A154615 a(n) = A061038(2*n) (bisection).
%F A154615 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
%F A154615 G.f.: x*(1+16*x+6*x^2+16*x^3+x^4)/((1-x)^3*(1+x)^3).
%F A154615 From _G. C. Greubel_, Jul 20 2017: (Start)
%F A154615 a(n) = (1/2)*(5 + 3*(-1)^n)*n^2.
%F A154615 E.g.f.: x*( (4*x +1)*cosh(x) + (x+4)*sinh(x) ). (End)
%F A154615 Sum_{n>=1} 1/a(n) = 13*Pi^2/96. - _Amiram Eldar_, Aug 13 2022
%t A154615 Join[{0}, Denominator[Table[(1/4)*(1 - 1/n^2), {n, 1, 50}]]] (* or *) Table[(1/2)*(5 + 3*(-1)^n)*n^2 {n,0,50}] (* _G. C. Greubel_, Jul 20 2017 *)
%o A154615 (PARI) for(n=0, 50, print1((1/2)*(5 + 3*(-1)^n)*n^2, ", ")) \\ _G. C. Greubel_, Jul 20 2017
%Y A154615 Cf. A000290, A016754, A022998, A061038.
%K A154615 nonn,easy,mult
%O A154615 0,3
%A A154615 _Paul Curtz_, Jan 13 2009
%E A154615 Edited, offset set to 1, and extended by _R. J. Mathar_, Sep 07 2009
%E A154615 a(0) added Oct 21 2009