A041324 Numerators of continued fraction convergents to sqrt(176).

13, 40, 53, 199, 5227, 15880, 21107, 79201, 2080333, 6320200, 8400533, 31521799, 827967307, 2515423720, 3343391027, 12545596801, 329528907853, 1001132320360, 1330661228213, 4993116004999, 131151677358187, 398448148079560, 529599825437747

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,398,0,0,0,-1).

Formula

G.f.: -(x^7-13*x^6+40*x^5-53*x^4-199*x^3-53*x^2-40*x-13) / ((x^4-20*x^2+1)*(x^4+20*x^2+1)). - Colin Barker, Nov 06 2013

a(n) = 398*a(n-4) - a(n-8) for n > 7. - Wesley Ivan Hurt, Oct 15 2017

Mathematica

Numerator[Convergents[Sqrt[176], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 0, 0, 398, 0, 0, 0, -1}, {13, 40, 53, 199, 5227, 15880, 21107, 79201}, 30]

Crossrefs

Cf. A041325.

Sequence in context: A168235 A258597 A299816 * A220083 A041326 A319088

Adjacent sequences: A041321 A041322 A041323 * A041325 A041326 A041327

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 06 2013

Status

approved