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A042810 Numerators of continued fraction convergents to sqrt(936). 2
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 (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, 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

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Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)