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A041537 Denominators of continued fraction convergents to sqrt(285). 2
1, 1, 8, 17, 127, 144, 4735, 4879, 38888, 82655, 617473, 700128, 23021569, 23721697, 189073448, 401868593, 3002153599, 3404022192, 111930863743, 115334885935, 919275065288, 1953885016511, 14596470180865, 16550355197376, 544207836496897, 560758191694273 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, 4862, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^10 -x^9 +8*x^8 -17*x^7 +127*x^6 -144*x^5 -127*x^4 -17*x^3 -8*x^2 -x -1) / ((x^4 -17*x^2 +1)*(x^8 +17*x^6 +288*x^4 +17*x^2 +1)). - Colin Barker, Nov 18 2013

a(n) = 4862*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

MATHEMATICA

Denominator[Convergents[Sqrt[285], 30]] (* Harvey P. Dale, Nov 08 2013 *)

CoefficientList[Series[-(x^10 - x^9 + 8 x^8 - 17 x^7 + 127 x^6 - 144 x^5 - 127 x^4 - 17 x^3 - 8 x^2 - x - 1)/((x^4 - 17 x^2 + 1) (x^8 + 17 x^6 + 288 x^4 + 17 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

PROG

(MAGMA) I:=[1, 1, 8, 17, 127, 144, 4735, 4879, 38888, 82655, 617473, 700128]; [n le 12 select I[n] else 4862*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

CROSSREFS

Cf. A041536, A176104, A040268.

Sequence in context: A097405 A192282 A088588 * A153315 A041126 A248289

Adjacent sequences:  A041534 A041535 A041536 * A041538 A041539 A041540

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 18 2013

STATUS

approved

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Last modified August 20 08:50 EDT 2018. Contains 313914 sequences. (Running on oeis4.)