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A041915
Denominators of continued fraction convergents to sqrt(479).
2
1, 1, 8, 9, 35, 79, 1694, 3467, 12095, 15562, 121029, 136591, 5857851, 5994442, 47818945, 53813387, 209259106, 472331599, 10128222685, 20728776969, 72314553592, 93043330561, 723617867519, 816661198080, 35023388186879, 35840049384959
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5978880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^22 -x^21 +8*x^20 -9*x^19 +35*x^18 -79*x^17 +1694*x^16 -3467*x^15 +12095*x^14 -15562*x^13 +121029*x^12 -136591*x^11 -121029*x^10 -15562*x^9 -12095*x^8 -3467*x^7 -1694*x^6 -79*x^5 -35*x^4 -9*x^3 -8*x^2 -x -1)/(x^24 -5978880*x^12 +1). - Vincenzo Librandi, Dec 27 2013
a(n) = 5978880*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 27 2013
MATHEMATICA
Denominator[Convergents[Sqrt[479], 30]] (* or *) CoefficientList[Series[-(x^22 - x^21 + 8 x^20 - 9 x^19 + 35 x^18 - 79 x^17 + 1694 x^16 - 3467 x^15 + 12095 x^14 - 15562 x^13 + 121029 x^12 - 136591 x^11 - 121029 x^10 - 15562 x^9 - 12095 x^8 - 3467 x^7 - 1694 x^6 - 79 x^5 - 35 x^4 - 9 x^3 - 8 x^2 - x - 1)/(x^24 - 5978880 x^12 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 27 2013 *)
PROG
(Magma) I:=[1, 1, 8, 9, 35, 79, 1694, 3467, 12095, 15562, 121029, 136591, 5857851, 5994442, 47818945, 53813387, 209259106, 472331599, 10128222685, 20728776969, 72314553592, 93043330561, 723617867519, 816661198080]; [n le 24 select I[n] else 5978880*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013
CROSSREFS
Cf. A041914.
Sequence in context: A050771 A120776 A041136 * A036764 A129548 A322797
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 27 2013
STATUS
approved