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A042924 Numerators of continued fraction convergents to sqrt(994). 2
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 (list; graph; refs; listen; history; text; internal format)
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 3013

STATUS

approved

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Last modified April 20 02:46 EDT 2019. Contains 322291 sequences. (Running on oeis4.)