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A041126 Numerators of continued fraction convergents to sqrt(72). 2
8, 17, 280, 577, 9512, 19601, 323128, 665857, 10976840, 22619537, 372889432, 768398401, 12667263848, 26102926097, 430314081400, 886731088897, 14618011503752, 30122754096401, 496582077046168, 1023286908188737, 16869172608065960, 34761632124320657 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (0,34,0,-1).

FORMULA

G.f.: -(x+1)*(x^2-9*x-8) / ((x^2-6*x+1)*(x^2+6*x+1)). - Colin Barker, Nov 05 2013

From Gerry Martens, Jul 11 2015: (Start)

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

a0(n) = (-4+3*sqrt(2))*(17+12*sqrt(2))^n-((4+3*sqrt(2))/(17+12*sqrt(2))^n).

a1(n) = (1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/2. (End)

MATHEMATICA

Numerator[Convergents[Sqrt[72], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

a0[n_] := (-4+3*Sqrt[2])*(17+12*Sqrt[2])^n-((4+3*Sqrt[2])/(17+12*Sqrt[2])^n) // Simplify

a1[n_] := (1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/2 // FullSimplify

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

CROSSREFS

Cf. A010524, A041127.

Sequence in context: A088588 A041537 A153315 * A248289 A176823 A316199

Adjacent sequences:  A041123 A041124 A041125 * A041127 A041128 A041129

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Colin Barker, Nov 05 2013

STATUS

approved

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Last modified February 19 13:03 EST 2020. Contains 332044 sequences. (Running on oeis4.)