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A041901 Denominators of continued fraction convergents to sqrt(472). 2
1, 1, 3, 4, 7, 11, 51, 266, 1115, 1381, 2496, 3877, 10250, 14127, 603584, 617711, 1839006, 2456717, 4295723, 6752440, 31305483, 163279855, 684424903, 847704758, 1532129661, 2379834419, 6291798499, 8671632918, 370500381055, 379172013973 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: -(x^26 -x^25 +3*x^24 -4*x^23 +7*x^22 -11*x^21 +51*x^20 -266*x^19 +1115*x^18 -1381*x^17 +2496*x^16 -3877*x^15 +10250*x^14 -14127*x^13 -10250*x^12 -3877*x^11 -2496*x^10 -1381*x^9 -1115*x^8 -266*x^7 -51*x^6 -11*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1)/(x^28 -613834*x^14 +1). - Vincenzo Librandi, Dec 26 2013

a(n) = 613834*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 26 2013

MATHEMATICA

Denominator[Convergents[Sqrt[472], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 4 x^23 + 7 x^22 - 11 x^21 + 51 x^20 - 266 x^19 + 1115 x^18 - 1381 x^17 + 2496 x^16 - 3877 x^15 + 10250 x^14 - 14127 x^13 - 10250 x^12 - 3877 x^11 - 2496 x^10 - 1381 x^9 - 1115 x^8 - 266 x^7 - 51 x^6 - 11 x^5 - 7 x^4 - 4 x^3 - 3 x^2 - x - 1)/(x^28 - 613834 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)

PROG

(MAGMA) I:=[1, 1, 3, 4, 7, 11, 51, 266, 1115, 1381, 2496, 3877, 10250, 14127, 603584, 617711, 1839006, 2456717, 4295723, 6752440, 31305483, 163279855, 684424903, 847704758, 1532129661, 2379834419, 6291798499, 8671632918]; [n le 28 select I[n] else 613834*Self(n-14)-Self(n-28): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

CROSSREFS

Cf. A041900.

Sequence in context: A042827 A041631 A042655 * A111518 A291853 A041153

Adjacent sequences:  A041898 A041899 A041900 * A041902 A041903 A041904

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 26 2013

STATUS

approved

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Last modified April 22 14:33 EDT 2019. Contains 322356 sequences. (Running on oeis4.)