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

0,2

Comments

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).

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).

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

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 *)

Crossrefs

Cf. A046176.

Sequence in context: A256799 A003743 A115491 * A183595 A054653 A061540

Adjacent sequences: A082402 A082403 A082404 * A082406 A082407 A082408

Keyword

nonn,easy

Author

Lekraj Beedassy, Apr 23 2003

Status

approved