A042842 Numerators of continued fraction convergents to sqrt(952).

30, 31, 185, 216, 1481, 1697, 9966, 11663, 709746, 721409, 4316791, 5038200, 34545991, 39584191, 232466946, 272051137, 16555535166, 16827586303, 100693466681, 117521052984, 805819784585, 923340837569, 5422523972430, 6345864809999, 386174412572370, 392520277382369

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, 23326, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (30 +31*x +185*x^2 +216*x^3 +1481*x^4 +1697*x^5 +9966*x^6 +11663*x^7 +9966*x^8 -1697*x^9 +1481*x^10 -216*x^11 +185*x^12 -31*x^13 +30*x^14 -x^15)/(1 -23326*x^8 +x^16). - Vincenzo Librandi, Dec 07 2013

a(n) = 23326*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 07 2013

Mathematica

Numerator[Convergents[Sqrt[952], 30]] (* or *)CoefficientList[Series[(30 + 31 x + 185 x^2 + 216 x^3 + 1481 x^4 + 1697 x^5 + 9966 x^6 + 11663 x^7 + 9966 x^8 - 1697 x^9 + 1481 x^10 - 216 x^11 + 185 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 23326 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 07 2013 *)

Prog

(Magma) I:=[30, 31, 185, 216, 1481, 1697, 9966, 11663, 709746, 721409, 4316791, 5038200, 34545991, 39584191, 232466946, 272051137]; [n le 16 select I[n] else 23326*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 07 2013

Crossrefs

Cf. A042843.

Sequence in context: A042830 A042838 A042836 * A042840 A042844 A042846

Adjacent sequences: A042839 A042840 A042841 * A042843 A042844 A042845

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 07 2013

Status

approved