A042607 Denominators of continued fraction convergents to sqrt(832).

1, 1, 6, 13, 32, 45, 617, 662, 1941, 4544, 24661, 29205, 1660141, 1689346, 10106871, 21903088, 53913047, 75816135, 1039522802, 1115338937, 3270200676, 7655740289, 41548902121, 49204642410, 2797008877081, 2846213519491, 17028076474536, 36902366468563

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, 0, 0, 0, 0, 0, 1684802, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^22 -x^21 +6*x^20 -13*x^19 +32*x^18 -45*x^17 +617*x^16 -662*x^15 +1941*x^14 -4544*x^13 +24661*x^12 -29205*x^11 -24661*x^10 -4544*x^9 -1941*x^8 -662*x^7 -617*x^6 -45*x^5 -32*x^4 -13*x^3 -6*x^2 -x -1) / ((x^2 -3*x -1)*(x^2 +3*x -1)*(x^4 -3*x^3 +10*x^2 +3*x +1)*(x^4 +11*x^2 +1)*(x^4 +3*x^3 +10*x^2 -3*x +1)*(x^8 -11*x^6 +120*x^4 -11*x^2 +1)). - Colin Barker, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[832], 30]] (* Vincenzo Librandi, Jan 25 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1684802, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 6, 13, 32, 45, 617, 662, 1941, 4544, 24661, 29205, 1660141, 1689346, 10106871, 21903088, 53913047, 75816135, 1039522802, 1115338937, 3270200676, 7655740289, 41548902121, 49204642410}, 30] (* Harvey P. Dale, Aug 06 2023 *)

Crossrefs

Cf. A042606, A040803.

Sequence in context: A192304 A343544 A147330 * A048693 A041068 A300430

Adjacent sequences: A042604 A042605 A042606 * A042608 A042609 A042610

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 19 2013

Status

approved