A041126 Numerators of continued fraction convergents to sqrt(72).

8, 17, 280, 577, 9512, 19601, 323128, 665857, 10976840, 22619537, 372889432, 768398401, 12667263848, 26102926097, 430314081400, 886731088897, 14618011503752, 30122754096401, 496582077046168, 1023286908188737, 16869172608065960, 34761632124320657

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