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 A088210 Numerators 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, 5, 17, 53, 157, 449, 1253, 3433, 9273, 24765, 65529, 172061, 448853, 1164409, 3006157, 7728337, 19794545, 50532469, 128621281, 326513669, 826887693, 2089505841, 5269572021, 13265211961, 33336792745, 83648953133, 209591807177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Denominators are A088211. Partial sums form A054459. Second differences form A026937. REFERENCES R. P. Grimaldi, Ternary strings with no consecutive 0's and no consecutive 1's, Congressus Numerantium, 205 (2011), 129-149. (See the foot of page 136.) LINKS FORMULA G.f.: (1+x)(1-x^2)/(1-2*x-x^2)^2. a(n) = P(n-1)+n*P(n) where P() = A000129 are the Pell numbers. EXAMPLE a(3)/A088211(3) = [2;2,2,4] = 53/22. CROSSREFS Cf. A000129, A088211, A054459, A026937. Sequence in context: A158896 A294781 A110318 * A135344 A222160 A027028 Adjacent sequences:  A088207 A088208 A088209 * A088211 A088212 A088213 KEYWORD frac,nonn AUTHOR Paul D. Hanna, Sep 23 2003 STATUS approved

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Last modified May 17 22:12 EDT 2021. Contains 343990 sequences. (Running on oeis4.)