A041764 Numerators of continued fraction convergents to sqrt(403).

20, 261, 542, 803, 2951, 3754, 14213, 17967, 50147, 669878, 26845267, 349658349, 726161965, 1075820314, 3953622907, 5029443221, 19041952570, 24071395791, 67184744152, 897473069767, 35966107534832, 468456871022583, 972879849579998, 1441336720602581

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, 1339756, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

a(n) = 1339756*a(n-10) - a(n-20) for n>19. - Bruno Berselli, Nov 07 2013

G.f.: -(x^19 -20*x^18 +261*x^17 -542*x^16 +803*x^15 -2951*x^14 +3754*x^13 -14213*x^12 +17967*x^11 -50147*x^10 -669878*x^9 -50147*x^8 -17967*x^7 -14213*x^6 -3754*x^5 -2951*x^4 -803*x^3 -542*x^2 -261*x -20) / (x^20 -1339756*x^10 +1). - Colin Barker, Dec 28 2013

Mathematica

Numerator[Convergents[Sqrt[403], 30]] (* Vincenzo Librandi, Nov 07 2013 *)

Prog

(PARI) Vec(-(x^19-20*x^18+261*x^17-542*x^16+803*x^15-2951*x^14+3754*x^13-14213*x^12+17967*x^11-50147*x^10-669878*x^9-50147*x^8-17967*x^7-14213*x^6-3754*x^5-2951*x^4-803*x^3-542*x^2-261*x-20)/(x^20-1339756*x^10+1)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Crossrefs

Cf. A041765, A040382.

Sequence in context: A081244 A025966 A356837 * A022111 A025943 A025961

Adjacent sequences: A041761 A041762 A041763 * A041765 A041766 A041767

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 28 2013

Status

approved