A041280 Numerators of continued fraction convergents to sqrt(153).

12, 25, 37, 99, 235, 569, 804, 2177, 53052, 108281, 161333, 430947, 1023227, 2477401, 3500628, 9478657, 230988396, 471455449, 702443845, 1876343139, 4455130123, 10786603385, 15241733508, 41270070401, 1005723423132, 2052716916665, 3058440339797, 8169597596259

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,4354,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x +1)*(x^14 -13*x^13 +38*x^12 -75*x^11 +174*x^10 -409*x^9 +978*x^8 -1782*x^7 -395*x^6 -409*x^5 -160*x^4 -75*x^3 -24*x^2 -13*x -12) / ((x^4 -8*x^2 -1)*(x^4 +8*x^2 -1)*(x^8 +66*x^4 +1)). - Colin Barker, Nov 06 2013

a(n) = 4354*a(n-8) - a(n-16). - Wesley Ivan Hurt, Oct 19 2021

Mathematica

Numerator[Convergents[Sqrt[153], 30]] (* Vincenzo Librandi, Nov 01 2013 *)

Crossrefs

Cf. A041281.

Sequence in context: A186620 A042851 A280324 * A132754 A250666 A363378

Adjacent sequences: A041277 A041278 A041279 * A041281 A041282 A041283

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 06 2013

Status

approved