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A158556 a(n) = 28*n^2 + 1.

%I A158556 #37 Jan 16 2025 20:55:48
%S A158556 1,29,113,253,449,701,1009,1373,1793,2269,2801,3389,4033,4733,5489,
%T A158556 6301,7169,8093,9073,10109,11201,12349,13553,14813,16129,17501,18929,
%U A158556 20413,21953,23549,25201,26909,28673,30493,32369,34301,36289,38333,40433,42589,44801,47069
%N A158556 a(n) = 28*n^2 + 1.
%C A158556 The identity (28*n^2 + 1)^2 - (196*n^2 + 14) * (2*n)^2 = 1 can be written as a(n)^2 - A158555(n)*A005843(n)^2 = 1.
%H A158556 Vincenzo Librandi, <a href="/A158556/b158556.txt">Table of n, a(n) for n = 0..1000</a>
%H A158556 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A158556 G.f.: (1 + 26*x + 29*x^2)/(1-x)^3.
%F A158556 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A158556 From _Amiram Eldar_, Mar 09 2023: (Start)
%F A158556 Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(28))*Pi/sqrt(28) + 1)/2.
%F A158556 Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(28))*Pi/sqrt(28) + 1)/2. (End)
%F A158556 From _Elmo R. Oliveira_, Jan 16 2025: (Start)
%F A158556 E.g.f.: exp(x)*(1 + 28*x + 28*x^2).
%F A158556 a(n) = A247541(2*n). (End)
%t A158556 LinearRecurrence[{3, -3, 1}, {1, 29, 113}, 50] (* _Vincenzo Librandi_, Mar 02 2012 *)
%t A158556 28*Range[0,40]^2+1 (* _Harvey P. Dale_, Jun 30 2022 *)
%o A158556 (Magma) I:=[1, 29, 113]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Mar 02 2012
%o A158556 (PARI) for(n=0, 40, print1(28*n^2+1", ")); \\ _Vincenzo Librandi_, Mar 02 2012
%Y A158556 Cf. A005843, A158555, A247541.
%K A158556 nonn,easy
%O A158556 0,2
%A A158556 _Vincenzo Librandi_, Mar 21 2009
%E A158556 Comment rewritten, a(0) added by _R. J. Mathar_, Oct 16 2009