A041204 Numerators of continued fraction convergents to sqrt(113).

10, 11, 21, 32, 85, 202, 287, 489, 776, 16009, 16785, 32794, 49579, 131952, 313483, 445435, 758918, 1204353, 24845978, 26050331, 50896309, 76946640, 204789589, 486525818, 691315407, 1177841225, 1869156632, 38560973865, 40430130497, 78991104362, 119421234859

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1552,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^17 -10*x^16 +11*x^15 -21*x^14 +32*x^13 -85*x^12 +202*x^11 -287*x^10 +489*x^9 +776*x^8 +489*x^7 +287*x^6 +202*x^5 +85*x^4 +32*x^3 +21*x^2 +11*x +10) / (x^18 +1552*x^9 -1). - Colin Barker, Nov 08 2013

Mathematica

Numerator[Convergents[Sqrt[113], 30]] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1552, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {10, 11, 21, 32, 85, 202, 287, 489, 776, 16009, 16785, 32794, 49579, 131952, 313483, 445435, 758918, 1204353}, 40] (* Harvey P. Dale, Sep 26 2020 *)

Crossrefs

Cf. A041205.

Sequence in context: A339138 A022100 A041475 * A041202 A324550 A214617

Adjacent sequences: A041201 A041202 A041203 * A041205 A041206 A041207

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 08 2013

Status

approved