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A195615 Numerators b(n) of Pythagorean approximations b(n)/a(n) to 2. 3
15, 273, 4895, 87841, 1576239, 28284465, 507544127, 9107509825, 163427632719, 2932589879121, 52623190191455, 944284833567073, 16944503814015855, 304056783818718321, 5456077604922913919, 97905340104793732225, 1756840044281364266127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A195500 for discussion and list of related sequences; see A195614 for Mathematica program.

LINKS

Colin Barker, Table of n, a(n) for n = 1..797

Index entries for linear recurrences with constant coefficients, signature (17,17,-1).

FORMULA

a(n) = 17*a(n-1)+17*a(n-2)-a(n-3). G.f.: -x*(x^2-18*x-15) / ((x+1)*(x^2-18*x+1)). - Colin Barker, Jun 04 2015

a(n) = ((-1)^n-(-2+sqrt(5))*(9+4*sqrt(5))^(-n)+(2+sqrt(5))*(9+4*sqrt(5))^n)/5. - Colin Barker, Mar 04 2016

PROG

(PARI) Vec(-x*(x^2-18*x-15)/((x+1)*(x^2-18*x+1)) + O(x^50)) \\ Colin Barker, Jun 04 2015

CROSSREFS

Cf. A195500, A195614, A007805.

Sequence in context: A013380 A013382 A227973 * A156091 A194728 A284077

Adjacent sequences:  A195612 A195613 A195614 * A195616 A195617 A195618

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 22 2011

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)