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A082405 a(n) = 34*a(n-1) - a(n-2); a(0)=0, a(1)=6.

%I A082405 #38 Jan 01 2024 11:17:53
%S A082405 0,6,204,6930,235416,7997214,271669860,9228778026,313506783024,
%T A082405 10650001844790,361786555939836,12290092900109634,417501372047787720,
%U A082405 14182756556724672846,481796221556591089044,16366888776367372354650
%N A082405 a(n) = 34*a(n-1) - a(n-2); a(0)=0, a(1)=6.
%C A082405 Sequence refers to inradius of primitive Pythagorean triangle with consecutive legs, even followed by odd. It has semiperimeter A046176(n+1) and area a(n)*A046176(n+1).
%H A082405 Indranil Ghosh, <a href="/A082405/b082405.txt">Table of n, a(n) for n = 0..652</a>
%H A082405 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A082405 Giovanni Lucca, <a href="https://ijgeometry.com/product/giovanni-lucca-circle-chains-inside-the-arbelos-and-integer-sequences/">Circle chains inside the arbelos and integer sequences</a>, Int'l J. Geom. (2023) Vol. 12, No. 1, 71-82.
%H A082405 Serge Perrine, <a href="http://article.scirea.org/pdf/11150.pdf">About the diophantine equation z^2 = 32y^2 - 16</a>, SCIREA Journal of Mathematics (2019) Vol. 4, Issue 5, 126-139.
%H A082405 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (34, -1).
%F A082405 For n > 1, a(n)/2 = A001652(2*n-1) - Sum_{k=0..n-1} A001333(4*k); e.g., 6930/2 = 4059 - (17+577). - _Charlie Marion_, Jul 31 2003
%F A082405 a(n) = A001109(2n).
%F A082405 G.f.: 6*x/(1 - 34*x + x^2). - _Philippe Deléham_, Nov 18 2008
%F A082405 a(n) = 6*A029547(n-1). - _R. J. Mathar_, Jun 07 2016
%t A082405 a[0] = 1; a[1] = 6; a[n_] := 34 a[n-1] - a[n-2]; Table[a[n], {n,0,15}] (* or *) LinearRecurrence[{34,-1}, {1,6}, 16] (* _Indranil Ghosh_, Feb 18 2017 *)
%Y A082405 Cf. A046176.
%K A082405 nonn,easy
%O A082405 0,2
%A A082405 _Lekraj Beedassy_, Apr 23 2003