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A041022 Numerators of continued fraction convergents to sqrt(15). 2
3, 4, 27, 31, 213, 244, 1677, 1921, 13203, 15124, 103947, 119071, 818373, 937444, 6443037, 7380481, 50725923, 58106404, 399364347, 457470751, 3144188853, 3601659604, 24754146477, 28355806081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

FORMULA

G.f.: (3+4*x+3*x^2-x^3)/(1-8*x^2+x^4).

From Gerry Martens, Jul 11 2015: (Start)

Interspersion of 2 sequences [a0(n),a1(n)] for n>0:

a0(n) = (-((4-sqrt(15))^n*(3+sqrt(15)))+(-3+sqrt(15))*(4+sqrt(15))^n)/2.

a1(n) = ((4-sqrt(15))^n+(4+sqrt(15))^n)/2. (End)

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[15], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)

Numerator[Convergents[Sqrt[15], 30]] (* Vincenzo Librandi, Oct 28 2013 *)

a0[n_] := (-((4-Sqrt[15])^n*(3+Sqrt[15]))+(-3+Sqrt[15])*(4+Sqrt[15])^n)/2 // Simplify

a1[n_] := ((4-Sqrt[15])^n+(4+Sqrt[15])^n)/2 // Simplify

Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)

CROSSREFS

Cf. A010472, A041023.

Sequence in context: A222112 A032832 A041021 * A157163 A042225 A094084

Adjacent sequences:  A041019 A041020 A041021 * A041023 A041024 A041025

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 8 06:50 EST 2016. Contains 278902 sequences.