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).
a(n)/2 are the y-values in Pellian solutions to x^2 - 32*y^2 = +1. The x-values are in A056771. - Patrick De Geest, Jun 14 2026
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
KEYWORD
nonn,easy,changed
AUTHOR
Lekraj Beedassy, Apr 23 2003
STATUS
approved