A145543 Denominators in continued fraction expansion of sqrt(3/5).

1, 4, 9, 31, 71, 244, 559, 1921, 4401, 15124, 34649, 119071, 272791, 937444, 2147679, 7380481, 16908641, 58106404, 133121449, 457470751, 1048062951, 3601659604, 8251382159, 28355806081, 64962994321, 223244789044, 511452572409, 1757602506271, 4026657584951

Offset: 1

Author

Gary W. Adamson, Oct 12 2008

Keywords

• nonn
• easy

Comments

A145542/a(n) tends to sqrt(3/5).

Examples

			Since the partial quotients of CF sqrt(3/5)= [1, 3, 2, 3, 2, 3,...] denominators are 1, 4, 9, 31, 71, 244, 559,...; given a(1) = 1, a(2) = 4.
		

Crossrefs

Cf. A145542.

Programs

Mathematica

Rest @ Denominator @ Convergents [Sqrt[3/5], 30] (* Amiram Eldar, Feb 26 2020 *)

Formula

Use the partial quotients of the continued fraction expansion of sqrt(3/5) as recursive operation multipliers, given a(1) = 1, a(2) = 4.

Empirical G.f.: x*(1+4*x+x^2-x^3)/(1-8*x^2+x^4). - Colin Barker, Jan 04 2012

Extensions

More terms from Amiram Eldar, Feb 26 2020