A041661 Denominators of continued fraction convergents to sqrt(349).

1, 1, 3, 22, 157, 336, 493, 18084, 18577, 55238, 405243, 2891939, 6189121, 9081060, 333107281, 342188341, 1017483963, 7464576082, 53269516537, 114003609156, 167273125693, 6135836134104, 6303109259797, 18742054653698, 137497491835683, 981224497503479

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, 18420, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^12 -x^11 +3*x^10 -22*x^9 +157*x^8 -336*x^7 +493*x^6 +336*x^5 +157*x^4 +22*x^3 +3*x^2 +x +1) / (x^14 +18420*x^7 -1). - Colin Barker, Nov 21 2013

a(n) = 18420*a(n-7) + a(n-14) for n>13. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[349], 30]] (* Vincenzo Librandi, Dec 22 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 18420, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 3, 22, 157, 336, 493, 18084, 18577, 55238, 405243, 2891939, 6189121, 9081060}, 30] (* Harvey P. Dale, Jun 20 2015 *)

Prog

(Magma) I:=[1, 1, 3, 22, 157, 336, 493, 18084, 18577, 55238, 405243, 2891939, 6189121, 9081060]; [n le 14 select I[n] else 18420*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041660, A040330.

Sequence in context: A037663 A091167 A037782 * A037586 A183259 A218668

Adjacent sequences: A041658 A041659 A041660 * A041662 A041663 A041664

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 21 2013

Status

approved