login
A041899
Denominators of continued fraction convergents to sqrt(471).
2
1, 1, 3, 7, 10, 37, 158, 2249, 9154, 29711, 38865, 107441, 253747, 361188, 15423643, 15784831, 46993305, 109771441, 156764746, 580065679, 2477027462, 35258450147, 143510828050, 465790934297, 609301762347, 1684394458991, 3978090680329, 5662485139320
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, 15677390, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^26 -x^25 +3*x^24 -7*x^23 +10*x^22 -37*x^21 +158*x^20 -2249*x^19 +9154*x^18 -29711*x^17 +38865*x^16 -107441*x^15 +253747*x^14 -361188*x^13 -253747*x^12 -107441*x^11 -38865*x^10 -29711*x^9 -9154*x^8 -2249*x^7 -158*x^6 -37*x^5 -10*x^4 -7*x^3 -3*x^2 -x -1)/(x^28 -15677390*x^14 +1). - Vincenzo Librandi, Dec 26 2013
a(n) = 15677390*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[471], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 7 x^23 + 10 x^22 - 37 x^21 + 158 x^20 - 2249 x^19 + 9154 x^18 - 29711 x^17 + 38865 x^16 - 107441 x^15 + 253747 x^14 - 361188 x^13 - 253747 x^12 - 107441 x^11 - 38865 x^10 - 29711 x^9 - 9154 x^8 - 2249 x^7 - 158 x^6 - 37 x^5 - 10 x^4 - 7 x^3 - 3 x^2 - x - 1)/(x^28 - 15677390 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)
PROG
(Magma) I:=[1, 1, 3, 7, 10, 37, 158, 2249, 9154, 29711, 38865, 107441, 253747, 361188, 15423643, 15784831, 46993305, 109771441, 156764746, 580065679, 2477027462, 35258450147, 143510828050, 465790934297, 609301762347, 1684394458991, 3978090680329, 5662485139320]; [n le 28 select I[n] else 15677390*Self(n-14)-Self(n-28): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
Cf. A041898.
Sequence in context: A146927 A193650 A041783 * A101397 A042229 A042373
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 26 2013
STATUS
approved