A041233 Denominators of continued fraction convergents to sqrt(128).

1, 3, 16, 51, 1138, 3465, 18463, 58854, 1313251, 3998607, 21306286, 67917465, 1515490516, 4614389013, 24587435581, 78376695756, 1748874742213, 5325000922395, 28373879354188, 90446638984959, 2018199937023286, 6145046450054817, 32743432187297371, 104375343011946930

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1154,0,0,0,-1).

Formula

From Vincenzo Librandi, Dec 13 2013: (Start)

G.f.: (1+3*x+16*x^2+51*x^3-16*x^4+3*x^5-x^6)/(1-1154*x^4+x^8).

a(n) = 1154*a(n-4) - a(n-8). (End)

Mathematica

Denominator[Convergents[Sqrt[128], 20]] (* Harvey P. Dale, Apr 01 2013 *)
CoefficientList[Series[(1 + 3 x + 16 x^2 + 51 x^3 - 16 x^4 + 3 x^5 - x^6)/(1 - 1154 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 13 2013 *)

Prog

(Magma) I:=[1, 3, 16, 51, 1138, 3465, 18463, 58854]; [n le 8 select I[n] else 1154*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041232.

Sequence in context: A004320 A089363 A000574 * A055194 A190730 A173052

Adjacent sequences: A041230 A041231 A041232 * A041234 A041235 A041236

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 13 2013

Status

approved