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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], ...
2
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
0,2
COMMENTS
Numerators are A088210.
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]
EXAMPLE
A088210(3)/a(3) = [2;2,2,4] = 53/22.
MATHEMATICA
LinearRecurrence[{4, -2, -4, -1}, {1, 2, 7, 22}, 30] (* Paolo Xausa, Feb 08 2024 *)
CROSSREFS
Sequence in context: A364539 A084264 A333678 * A071684 A290917 A060816
KEYWORD
frac,nonn
AUTHOR
Paul D. Hanna, Sep 23 2003
STATUS
approved