A042924 Numerators of continued fraction convergents to sqrt(994).

31, 32, 63, 536, 599, 1135, 70969, 72104, 143073, 1216688, 1359761, 2576449, 161099599, 163676048, 324775647, 2761881224, 3086656871, 5848538095, 365696018761, 371544556856, 737240575617, 6269469161792, 7006709737409, 13276178899201, 830129801487871

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, 2270, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (31 + 32*x + 63*x^2 + 536*x^3 + 599*x^4 + 1135*x^5 + 599*x^6 - 536*x^7 + 63*x^8 - 32*x^9 + 31*x^10 - x^11)/(1 - 2270*x^6 + x^12). - Vincenzo Librandi, Dec 09 2013

a(n) = 2270*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 09 2013

Mathematica

Numerator[Convergents[Sqrt[994], 30]] (* or *) CoefficientList[Series[(31 + 32 x + 63 x^2 + 536 x^3 + 599 x^4 + 1135 x^5 + 599 x^6 - 536 x^7 + 63 x^8 - 32 x^9 + 31 x^10 - x^11)/(1 - 2270 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 2270, 0, 0, 0, 0, 0, -1}, {31, 32, 63, 536, 599, 1135, 70969, 72104, 143073, 1216688, 1359761, 2576449}, 30] (* Harvey P. Dale, Jun 23 2017 *)

Prog

(Magma) I:=[31, 32, 63, 536, 599, 1135, 70969, 72104, 143073, 1216688, 1359761, 2576449]; [n le 12 select I[n] else 2270*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 09 2013

Crossrefs

Cf. A042925.

Sequence in context: A042932 A042928 A042926 * A042922 A171235 A248815

Adjacent sequences: A042921 A042922 A042923 * A042925 A042926 A042927

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 09 2013

Status

approved