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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
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 613834, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
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
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 26 2013
STATUS
approved