A041403 Denominators of continued fraction convergents to sqrt(216).

1, 1, 3, 10, 23, 33, 947, 980, 2907, 9701, 22309, 32010, 918589, 950599, 2819787, 9409960, 21639707, 31049667, 891030383, 922080050, 2735190483, 9127651499, 20990493481, 30118144980, 864298552921, 894416697901, 2653131948723, 8853812544070, 20360757036863

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,970,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -x^9 +3*x^8 -10*x^7 +23*x^6 -33*x^5 -23*x^4 -10*x^3 -3*x^2 -x -1) / ((x^4 -10*x^2 +1)*(x^8 +10*x^6 +99*x^4 +10*x^2 +1)). - Colin Barker, Nov 17 2013

a(n) = 970*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[216], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 1, 3, 10, 23, 33, 947, 980, 2907, 9701, 22309, 32010]; [n le 12 select I[n] else 970*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041402, A040201.

Sequence in context: A292921 A270470 A166119 * A077126 A172113 A172112

Adjacent sequences: A041400 A041401 A041402 * A041404 A041405 A041406

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved