A088211 Denominators of convergents of the continued fraction with the n+1 partial quotients: [2;2,2,...(n 2's)...,2,n+1], starting with [1], [2;2], [2;2,3], [2;2,2,4], ...

1, 2, 7, 22, 65, 186, 519, 1422, 3841, 10258, 27143, 71270, 185921, 482314, 1245191, 3201182, 8199169, 20931234, 53276679, 135246390, 342508097, 865501658, 2182728199, 5494630702, 13808551681, 34648530866, 86815769095, 217237177222

Offset: 0

Author

Paul D. Hanna, Sep 23 2003

Keywords

• frac
• nonn

Comments

Numerators are A088210.

Examples

			A088210(3)/a(3) = [2;2,2,4] = 53/22.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,-1).

Crossrefs

Cf. A088210, A000129.

Programs

Mathematica

LinearRecurrence[{4, -2, -4, -1}, {1, 2, 7, 22}, 30] (* Paolo Xausa, Feb 08 2024 *)

Formula

G.f.: (1-2*x+x^2+2*x^3)/(1-2*x-x^2)^2.

a(n) = A000129(n+1) + (n-1)*A000129(n), where A000129 are the Pell numbers. [Corrected by Paolo Xausa, Feb 08 2024]