A158062 - OEIS

%I #27 Nov 09 2022 01:41:02

%S 34,140,318,568,890,1284,1750,2288,2898,3580,4334,5160,6058,7028,8070,

%T 9184,10370,11628,12958,14360,15834,17380,18998,20688,22450,24284,

%U 26190,28168,30218,32340,34534,36800,39138,41548,44030,46584,49210,51908

%N a(n) = 36*n^2 - 2*n.

%C The identity (36*n - 1)^2 - (36*n^2 - 2*n)*6^2 = 1 can be written as (A044102(n+1) - 1)^2 - a(n)*6^2 = 1. - _Vincenzo Librandi_, Feb 11 2012

%C The continued fraction expansion of sqrt(a(n)) is [6n-1; {1, 4, 1, 12n-2}]. - _Magus K. Chu_, Nov 08 2022

%H Vincenzo Librandi, <a href="/A158062/b158062.txt">Table of n, a(n) for n = 1..10000</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*(6^2*t-2)).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: x*(-34 - 38*x)/(x-1)^3. - _Vincenzo Librandi_, Feb 11 2012

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 11 2012

%t LinearRecurrence[{3, -3, 1}, {34, 140, 318}, 50] (* _Vincenzo Librandi_, Feb 11 2012 *)

%o (Magma)[36*n^2 - 2*n: n in [1..50]]

%o (PARI) for(n=1, 50, print1(36*n^2 - 2*n ", ")); \\ _Vincenzo Librandi_, Feb 11 2012

%Y Cf. A044102.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 12 2009