A042853 Denominators of continued fraction convergents to sqrt(957).

1, 1, 15, 31, 449, 480, 29249, 29729, 445455, 920639, 13334401, 14255040, 868636801, 882891841, 13229122575, 27341136991, 396005040449, 423346177440, 25796775686849, 26220121864289, 392878481786895, 811977085438079, 11760557677920001, 12572534763358080

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,29698,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -x^9 +15*x^8 -31*x^7 +449*x^6 -480*x^5 -449*x^4 -31*x^3 -15*x^2 -x -1) / ((x^4 -31*x^2 +1)*(x^8 +31*x^6 +960*x^4 +31*x^2 +1)). - Colin Barker, Dec 25 2013

a(n) = 29698*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 25 2013

Mathematica

Denominator[Convergents[Sqrt[957], 30]] (* Vincenzo Librandi, Dec 25 2013 *)

Prog

(Magma) I:=[1, 1, 15, 31, 449, 480, 29249, 29729, 445455, 920639, 13334401, 14255040]; [n le 12 select I[n] else 29698*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013

Crossrefs

Cf. A042852, A040926.

Sequence in context: A102955 A041444 A041446 * A065575 A041448 A157767

Adjacent sequences: A042850 A042851 A042852 * A042854 A042855 A042856

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 25 2013

Status

approved