A042810 Numerators of continued fraction convergents to sqrt(936).

30, 31, 61, 153, 979, 2111, 3090, 5201, 315150, 320351, 635501, 1591353, 10183619, 21958591, 32142210, 54100801, 3278190270, 3332291071, 6610481341, 16553253753, 105930003859, 228413261471, 334343265330, 562756526801, 34099734873390, 34662491400191, 68762226273581

Offset

0,1

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, 10402, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (30 +31*x +61*x^2 +153*x^3 +979*x^4 +2111*x^5 +3090*x^6 +5201*x^7 +3090*x^8 -2111*x^9 +979*x^10 -153*x^11 +61*x^12 -31*x^13 +30*x^14 -x^15)/(1 -10402*x^8 +x^16). - Vincenzo Librandi, Dec 05 2013

a(n) = 10402*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 05 2013

Mathematica

Numerator[Convergents[Sqrt[936], 30]] (* Harvey P. Dale, Feb 06 2012 *)
CoefficientList[Series[(30 + 31 x + 61 x^2 + 153 x^3 + 979 x^4 + 2111 x^5 + 3090 x^6 + 5201 x^7 + 3090 x^8 - 2111 x^9 + 979 x^10 - 153 x^11 + 61 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 10402 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 05 2013 *)

Prog

(Magma) I:=[30, 31, 61, 153, 979, 2111, 3090, 5201, 315150, 320351, 635501, 1591353, 10183619, 21958591, 32142210, 54100801]; [n le 16 select I[n] else 10402*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 05 2013

Crossrefs

Cf. A042811.

Sequence in context: A042816 A042818 A042808 * A042806 A042804 A042802

Adjacent sequences: A042807 A042808 A042809 * A042811 A042812 A042813

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 05 2013

Status

approved