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A042822 Numerators of continued fraction convergents to sqrt(942). 2
30, 31, 92, 399, 8072, 32687, 73446, 106133, 6441426, 6547559, 19536544, 84693735, 1713411244, 6938338711, 15590088666, 22528427377, 1367295731286, 1389824158663, 4146944048612, 17977600353111, 363698951110832, 1472773404796439, 3309245760703710, 4782019165500149 (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, 212266, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: (30 +31*x +92*x^2 +399*x^3 +8072*x^4 +32687*x^5 +73446*x^6 +106133*x^7 +73446*x^8 -32687*x^9 +8072*x^10 -399*x^11 +92*x^12 -31*x^13 +30*x^14 -x^15)/(1 -212266*x^8 +x^16). - Vincenzo Librandi, Dec 05 2013

a(n) = 212266*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 05 2013

MATHEMATICA

Numerator/@Convergents[Sqrt[942], 30] (* Harvey P. Dale, Jul 18 2011 *)

CoefficientList[Series[(30 + 31 x + 92 x^2 + 399 x^3 + 8072 x^4 + 32687 x^5 + 73446 x^6 + 106133 x^7 + 73446 x^8 - 32687 x^9 + 8072 x^10 - 399 x^11 + 92 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 212266 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 05 2013 *)

PROG

(MAGMA) I:=[30, 31, 92, 399, 8072, 32687, 73446, 106133, 6441426, 6547559, 19536544, 84693735, 1713411244, 6938338711, 15590088666, 22528427377]; [n le 16 select I[n] else 212266*Self(n-8)-Self(n-16): n in [1..30]]; //  Vincenzo Librandi, Dec 05 2013

CROSSREFS

Cf. A042823.

Sequence in context: A042826 A042828 A042824 * A042820 A042834 A042832

Adjacent sequences:  A042819 A042820 A042821 * A042823 A042824 A042825

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 June 22 17:19 EDT 2018. Contains 305672 sequences. (Running on oeis4.)