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%I #14 Feb 08 2024 09:46:19
%S 1,2,7,22,65,186,519,1422,3841,10258,27143,71270,185921,482314,
%T 1245191,3201182,8199169,20931234,53276679,135246390,342508097,
%U 865501658,2182728199,5494630702,13808551681,34648530866,86815769095,217237177222
%N 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], ...
%C Numerators are A088210.
%H Paolo Xausa, <a href="/A088211/b088211.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-4,-1).
%F G.f.: (1-2*x+x^2+2*x^3)/(1-2*x-x^2)^2.
%F a(n) = A000129(n+1) + (n-1)*A000129(n), where A000129 are the Pell numbers. [Corrected by _Paolo Xausa_, Feb 08 2024]
%e A088210(3)/a(3) = [2;2,2,4] = 53/22.
%t LinearRecurrence[{4, -2, -4, -1}, {1, 2, 7, 22}, 30] (* _Paolo Xausa_, Feb 08 2024 *)
%Y Cf. A088210, A000129.
%K frac,nonn
%O 0,2
%A _Paul D. Hanna_, Sep 23 2003
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