A041717 Denominators of continued fraction convergents to sqrt(378).

1, 2, 7, 9, 43, 52, 199, 450, 17299, 35048, 122443, 157491, 752407, 909898, 3482101, 7874100, 302697901, 613269902, 2142507607, 2755777509, 13165617643, 15921395152, 60929803099, 137781001350, 5296607854399, 10730996710148, 37489597984843, 48220594694991

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,17498,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -2*x^13 +7*x^12 -9*x^11 +43*x^10 -52*x^9 +199*x^8 -450*x^7 -199*x^6 -52*x^5 -43*x^4 -9*x^3 -7*x^2 -2*x -1) / (x^16 -17498*x^8 +1). - Colin Barker, Nov 22 2013

a(n) = 17498*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[378], 30]] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 2, 7, 9, 43, 52, 199, 450, 17299, 35048, 122443, 157491, 752407, 909898, 3482101, 7874100]; [n le 16 select I[n] else 17498*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041716, A040358.

Sequence in context: A125770 A042063 A360734 * A002353 A041073 A079942

Adjacent sequences: A041714 A041715 A041716 * A041718 A041719 A041720

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved