A042374 Numerators of continued fraction convergents to sqrt(714).

26, 27, 80, 107, 187, 481, 668, 1149, 2966, 4115, 216946, 221061, 659068, 880129, 1539197, 3958523, 5497720, 9456243, 24410206, 33866449, 1785465554, 1819332003, 5424129560, 7243461563, 12667591123, 32578643809, 45246234932, 77824878741, 200895992414

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,8230,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^19 -26*x^18 +27*x^17 -80*x^16 +107*x^15 -187*x^14 +481*x^13 -668*x^12 +1149*x^11 -2966*x^10 -4115*x^9 -2966*x^8 -1149*x^7 -668*x^6 -481*x^5 -187*x^4 -107*x^3 -80*x^2 -27*x -26) / (x^20 -8230*x^10 +1). - Colin Barker, Dec 09 2013

a(n) = 8230*a(n-10) - a(n-20). - Wesley Ivan Hurt, Sep 07 2022

Mathematica

Numerator[Convergents[Sqrt[714], 30]] (* Vincenzo Librandi, Nov 22 2013 *)

Crossrefs

Cf. A042375, A040687.

Sequence in context: A042352 A304007 A305357 * A042376 A042372 A042370

Adjacent sequences: A042371 A042372 A042373 * A042375 A042376 A042377

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 09 2013

Status

approved