A041106 Numerators of continued fraction convergents to sqrt(61).

7, 8, 39, 125, 164, 453, 1070, 1523, 5639, 24079, 29718, 440131, 469849, 2319527, 7428430, 9747957, 26924344, 63596645, 90520989, 335159612, 1431159437, 1766319049, 26159626123, 27925945172, 137863406811, 441516165605, 579379572416, 1600275310437

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,59436,0,0,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^21 -7*x^20 +8*x^19 -39*x^18 +125*x^17 -164*x^16 +453*x^15 -1070*x^14 +1523*x^13 -5639*x^12 +24079*x^11 +29718*x^10 +24079*x^9 +5639*x^8 +1523*x^7 +1070*x^6 +453*x^5 +164*x^4 +125*x^3 +39*x^2 +8*x +7) / (x^22 +59436*x^11 -1). - Colin Barker, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[61], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Crossrefs

Cf. A010514, A041107, A010145, A020818.

Sequence in context: A122605 A037953 A296636 * A303732 A119453 A047192

Adjacent sequences: A041103 A041104 A041105 * A041107 A041108 A041109

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved