cp's OEIS Frontend

A158574 a(n) = 256*n^2 + 16.

%I A158574 #28 Mar 09 2023 02:45:20
%S A158574 16,272,1040,2320,4112,6416,9232,12560,16400,20752,25616,30992,36880,
%T A158574 43280,50192,57616,65552,74000,82960,92432,102416,112912,123920,
%U A158574 135440,147472,160016,173072,186640,200720,215312,230416,246032,262160,278800,295952,313616,331792
%N A158574 a(n) = 256*n^2 + 16.
%C A158574 The identity (32*n^2 + 1)^2 - (256*n^2 + 16)*(2*n)^2 = 1 can be written as A158575(n)^2 - a(n)*A005843(n)^2 = 1.
%H A158574 Vincenzo Librandi, <a href="/A158574/b158574.txt">Table of n, a(n) for n = 0..10000</a>
%H A158574 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A158574 G.f.: 16*(1 + 14*x + 17*x^2)/(1-x)^3.
%F A158574 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A158574 From _Amiram Eldar_, Mar 09 2023: (Start)
%F A158574 Sum_{n>=0} 1/a(n) = (coth(Pi/4)*Pi/4 + 1)/32.
%F A158574 Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/4)*Pi/4 + 1)/32. (End)
%t A158574 LinearRecurrence[{3, -3, 1}, {16, 272, 1040}, 50] (* _Vincenzo Librandi_, Feb 15 2012 *)
%o A158574 (Magma) I:=[16, 272, 1040]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 15 2012
%o A158574 (PARI) for(n=0, 50, print1(256*n+16", ")); \\ _Vincenzo Librandi_, Feb 15 2012
%Y A158574 Cf. A005843, A158575.
%K A158574 nonn,easy
%O A158574 0,1
%A A158574 _Vincenzo Librandi_, Mar 21 2009
%E A158574 Comment rewritten, a(0) added by _R. J. Mathar_, Oct 16 2009