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%I #40 Sep 08 2022 08:45:28
%S 15,31,47,63,79,95,111,127,143,159,175,191,207,223,239,255,271,287,
%T 303,319,335,351,367,383,399,415,431,447,463,479,495,511,527,543,559,
%U 575,591,607,623,639,655,671,687,703,719,735,751,767,783,799,815,831,847
%N a(n) = 16*n + 15.
%C The identity (16*n + 15)^2 - (16*(n+1)^2 - 2*(n+1))*4^2 = 1 can be written as a(n)^2 - A158058(n+1)*4^2 = 1. - _Vincenzo Librandi_, Feb 01 2012
%C a(n-3), n >= 3, appears in the third column of triangle A239126 related to the Collatz problem. - _Wolfdieter Lang_, Mar 14 2014
%H Vincenzo Librandi, <a href="/A125169/b125169.txt">Table of n, a(n) for n = 0..10000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(4^2*t-2)).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1) - a(n-2); a(0)=15, a(1)=31. - _Harvey P. Dale_, Jan 03 2012
%F O.g.f: (15 + x)/(1 - x)^2. - _Wolfdieter Lang_, Mar 14 2014
%t Table[16n + 15, {n, 0, 100}]
%t LinearRecurrence[{2,-1},{15,31},100] (* or *) Range[15,1620,16] (* _Harvey P. Dale_, Jan 03 2012 *)
%o (Magma) I:=[15, 31]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // _Vincenzo Librandi_, Jan 04 2012
%o (PARI) a(n) = 16*n + 15 \\ _Vincenzo Librandi_, Jan 04 2012
%Y Cf. A158058.
%K nonn,easy
%O 0,1
%A _Artur Jasinski_, Nov 22 2006
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