A042822 Numerators of continued fraction convergents to sqrt(942).

30, 31, 92, 399, 8072, 32687, 73446, 106133, 6441426, 6547559, 19536544, 84693735, 1713411244, 6938338711, 15590088666, 22528427377, 1367295731286, 1389824158663, 4146944048612, 17977600353111, 363698951110832, 1472773404796439, 3309245760703710, 4782019165500149

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