A082405 a(n) = 34*a(n-1) - a(n-2); a(0)=0, a(1)=6.
0, 6, 204, 6930, 235416, 7997214, 271669860, 9228778026, 313506783024, 10650001844790, 361786555939836, 12290092900109634, 417501372047787720, 14182756556724672846, 481796221556591089044, 16366888776367372354650
Offset: 0
Links
- Indranil Ghosh, Table of n, a(n) for n = 0..652
- Tanya Khovanova, Recursive Sequences
- Giovanni Lucca, Circle chains inside the arbelos and integer sequences, Int'l J. Geom. (2023) Vol. 12, No. 1, 71-82.
- Serge Perrine, About the diophantine equation z^2 = 32y^2 - 16, SCIREA Journal of Mathematics (2019) Vol. 4, Issue 5, 126-139.
- Index entries for linear recurrences with constant coefficients, signature (34, -1).
Crossrefs
Cf. A046176.
Programs
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Mathematica
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 *)
Formula
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
a(n) = A001109(2n).
G.f.: 6*x/(1 - 34*x + x^2). - Philippe Deléham, Nov 18 2008
a(n) = 6*A029547(n-1). - R. J. Mathar, Jun 07 2016
Comments