A041952 Numerators of continued fraction convergents to sqrt(499).

22, 45, 67, 1452, 1519, 4490, 199079, 402648, 601727, 13038915, 13640642, 40320199, 1787729398, 3615778995, 5403508393, 117089455248, 122492963641, 362075382530, 16053809794961, 32469694972452, 48523504767413, 1051463295088125, 1099986799855538

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, 8980, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^11 -22*x^10 +45*x^9 -67*x^8 +1452*x^7 -1519*x^6 -4490*x^5 -1519*x^4 -1452*x^3 -67*x^2 -45*x -22) / (x^12 -8980*x^6 +1). - Colin Barker, Nov 28 2013

a(n) = 8980*a(n-6)-a(n-12). - Wesley Ivan Hurt, May 27 2021

Mathematica

Numerator[Convergents[Sqrt[499], 30]] (* Vincenzo Librandi, Nov 12 2013 *)

Crossrefs

Cf. A041953, A040476.

Sequence in context: A335468 A041956 A041954 * A195149 A291557 A165309

Adjacent sequences: A041949 A041950 A041951 * A041953 A041954 A041955

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved