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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

Table of n, a(n) for n=0..26.

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 February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)