%I #34 Sep 08 2022 08:45:56

%S 3,41,571,7953,110771,1542841,21489003,299303201,4168755811,

%T 58063278153,808717138331,11263976658481,156886956080403,

%U 2185153408467161,30435260762459851,423908497265970753,5904283700961130691,82236063316189858921,1145400602725696894203

%N a(n) gives y-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2 for positive x.

%C (a(n)-1)/2 gives indices of triangular numbers which are also pentagonal (A046175).

%H Vincenzo Librandi, <a href="/A189356/b189356.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-1).

%F a(n) = 14*a(n-1) - a(n-2).

%F G.f.: x*(3-x)/(1-14*x+x^2). - _Bruno Berselli_, May 03 2011

%t LinearRecurrence[{14,-1}, {3, 41}, 19] (* _Bruno Berselli_, Nov 11 2011 *)

%o (Magma) [n le 2 select 38*n-35 else 14*Self(n-1)-Self(n-2): n in [1..19]]; // _Bruno Berselli_, May 03 2011

%Y Cf. A081065, A046174, A046175.

%K nonn

%O 1,1

%A _Sture Sjöstedt_, May 02 2011

%E Extended by _T. D. Noe_, May 02 2011