A041948 Numerators of continued fraction convergents to sqrt(497).

22, 67, 156, 379, 2051, 12685, 65476, 143637, 352750, 1201887, 53235778, 160909221, 375054220, 911017661, 4930142525, 30491872811, 157389506580, 345270885971, 847931278522, 2889064721537, 127966779026150, 386789401799987, 901545582626124, 2189880567052235

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, 2403774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^19 -22*x^18 +67*x^17 -156*x^16 +379*x^15 -2051*x^14 +12685*x^13 -65476*x^12 +143637*x^11 -352750*x^10 -1201887*x^9 -352750*x^8 -143637*x^7 -65476*x^6 -12685*x^5 -2051*x^4 -379*x^3 -156*x^2 -67*x -22) / (x^20 -2403774*x^10 +1). - Colin Barker, Nov 27 2013

Mathematica

Numerator[Convergents[Sqrt[497], 30]] (* Vincenzo Librandi, Nov 12 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 2403774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {22, 67, 156, 379, 2051, 12685, 65476, 143637, 352750, 1201887, 53235778, 160909221, 375054220, 911017661, 4930142525, 30491872811, 157389506580, 345270885971, 847931278522, 2889064721537}, 30] (* Harvey P. Dale, Dec 11 2025 *)

Crossrefs

Cf. A041949, A040474.

Sequence in context: A164136 A041946 A303858 * A002757 A346854 A041950

Adjacent sequences: A041945 A041946 A041947 * A041949 A041950 A041951

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved