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A042842 Numerators of continued fraction convergents to sqrt(952). 2
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 (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, 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

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Last modified August 18 20:29 EDT 2018. Contains 313840 sequences. (Running on oeis4.)