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A041877
Denominators of continued fraction convergents to sqrt(460).
2
1, 2, 9, 29, 38, 105, 1088, 2281, 3369, 12388, 52921, 118230, 5018581, 10155392, 45640149, 147075839, 192715988, 532507815, 5517794138, 11568096091, 17085890229, 62825766778, 268388957341, 599603681460, 25451743578661, 51503090838782, 231464106933789
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5071502, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (1 +2*x +9*x^2 +29*x^3 +38*x^4 +105*x^5 +1088*x^6 +2281*x^7 +3369*x^8 +12388*x^9 +52921*x^10 +118230*x^11 -52921*x^12 +12388*x^13 -3369*x^14 +2281*x^15 -1088*x^16 +105*x^17 -38*x^18 +29*x^19 -9*x^20 +2*x^21 -x^22)/(1 -5071502*x^12 +x^24). - Vincenzo Librandi, Dec 26 2013
a(n) = 5071502*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[460], 30]] (* or *) CoefficientList[Series[(1 + 2 x + 9 x^2 + 29 x^3 + 38 x^4 + 105 x^5 + 1088 x^6 + 2281 x^7 + 3369 x^8 + 12388 x^9 + 52921 x^10 + 118230 x^11 - 52921 x^12 + 12388 x^13 - 3369 x^14 + 2281 x^15 - 1088 x^16 + 105 x^17 - 38 x^18 + 29 x^19 - 9 x^20 + 2 x^21 - x^22)/(1 -5071502 x^12 + x^24), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 26 2013 *)
PROG
(Magma) I:=[1, 2, 9, 29, 38, 105, 1088, 2281, 3369, 12388, 52921, 118230, 5018581, 10155392, 45640149, 147075839, 192715988, 532507815, 5517794138, 11568096091, 17085890229, 62825766778, 268388957341, 599603681460]; [n le 24 select I[n] else 5071502*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
Cf. A041876.
Sequence in context: A002747 A110377 A338436 * A090208 A123058 A212272
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 26 2013
STATUS
approved