A041553 Denominators of continued fraction convergents to sqrt(294).

1, 6, 7, 34, 41, 280, 9561, 57646, 67207, 326474, 393681, 2688560, 91804721, 553516886, 645321607, 3134803314, 3780124921, 25815552840, 881508921481, 5314869081726, 6196378003207, 30100381094554, 36296759097761, 247880935681120, 8464248572255841

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,9602,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-6*x^9+7*x^8-34*x^7+41*x^6-280*x^5-41*x^4-34*x^3-7*x^2-6*x-1) / ((x^6-98*x^3+1)*(x^6+98*x^3+1)). - Colin Barker, Nov 18 2013

a(n) = 9602*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[294 ], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 6, 7, 34, 41, 280, 9561, 57646, 67207, 326474, 393681, 2688560]; [n le 12 select I[n] else 9602*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041552, A040276.

Sequence in context: A292106 A037375 A159582 * A047190 A359530 A237711

Adjacent sequences: A041550 A041551 A041552 * A041554 A041555 A041556

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved