A041949 Denominators of continued fraction convergents to sqrt(497).

1, 3, 7, 17, 92, 569, 2937, 6443, 15823, 53912, 2387951, 7217765, 16823481, 40864727, 221147116, 1367747423, 7059884231, 15487515885, 38034916001, 129592263888, 5740094527073, 17349875845107, 40439846217287, 98229568279681, 531587687615692

Offset

0,2

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^18 -3*x^17 +7*x^16 -17*x^15 +92*x^14 -569*x^13 +2937*x^12 -6443*x^11 +15823*x^10 -53912*x^9 -15823*x^8 -6443*x^7 -2937*x^6 -569*x^5 -92*x^4 -17*x^3 -7*x^2 -3*x -1) / (x^20 -2403774*x^10 +1). - Colin Barker, Nov 27 2013

a(n) = 2403774*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[497], 30]] (* Vincenzo Librandi, Dec 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 2403774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 3, 7, 17, 92, 569, 2937, 6443, 15823, 53912, 2387951, 7217765, 16823481, 40864727, 221147116, 1367747423, 7059884231, 15487515885, 38034916001, 129592263888}, 30] (* Harvey P. Dale, Mar 25 2026 *)

Prog

(Magma) I:=[1, 3, 7, 17, 92, 569, 2937, 6443, 15823, 53912, 2387951, 7217765, 16823481, 40864727, 221147116, 1367747423, 7059884231, 15487515885, 38034916001, 129592263888]; [n le 20 select I[n] else 2403774*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041948, A040474.

Sequence in context: A128343 A106877 A383027 * A222452 A218165 A384767

Adjacent sequences: A041946 A041947 A041948 * A041950 A041951 A041952

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved