A042491 Denominators of continued fraction convergents to sqrt(773).

1, 1, 5, 66, 71, 208, 487, 695, 9522, 38783, 48305, 2647253, 2695558, 13429485, 177278863, 190708348, 558695559, 1308099466, 1866795025, 25576434791, 104172534189, 129748968980, 7110616859109, 7240365828089, 36072080171465, 476177408057134, 512249488228599

Offset

0,3

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, 2686036, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^20 -x^19 +5*x^18 -66*x^17 +71*x^16 -208*x^15 +487*x^14 -695*x^13 +9522*x^12 -38783*x^11 +48305*x^10 +38783*x^9 +9522*x^8 +695*x^7 +487*x^6 +208*x^5 +71*x^4 +66*x^3 +5*x^2 +x +1) / (x^22 +2686036*x^11 -1). - Colin Barker, Dec 15 2013

a(n) = 2686036*a(n-11) + a(n-22). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[773], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

Prog

(Magma) I:=[1, 1, 5, 66, 71, 208, 487, 695, 9522, 38783, 48305, 2647253, 2695558, 13429485, 177278863, 190708348, 558695559, 1308099466, 1866795025, 25576434791, 104172534189, 129748968980]; [n le 22 select I[n] else 2686036*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A042490, A040745.

Sequence in context: A195516 A167536 A237887 * A183899 A263784 A263785

Adjacent sequences: A042488 A042489 A042490 * A042492 A042493 A042494

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 15 2013

Status

approved