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A042685
Denominators of continued fraction convergents to sqrt(872).
2
1, 1, 2, 15, 17, 236, 253, 2007, 2260, 4267, 249746, 254013, 503759, 3780326, 4284085, 59473431, 63757516, 505776043, 569533559, 1075309602, 62937490475, 64012800077, 126950290552, 952664833941, 1079615124493, 14987661452350, 16067276576843, 127458597490251
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 252006, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^18 -x^17 +2*x^16 -15*x^15 +17*x^14 -236*x^13 +253*x^12 -2007*x^11 +2260*x^10 -4267*x^9 -2260*x^8 -2007*x^7 -253*x^6 -236*x^5 -17*x^4 -15*x^3 -2*x^2 -x -1) / ((x^10 -502*x^5 -1)*(x^10 +502*x^5 -1)). - Colin Barker, Dec 21 2013
a(n) = 252006*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 21 2013
MATHEMATICA
Denominator/@Convergents[Sqrt[872], 30] (* Harvey P. Dale, Mar 14 2011 *)
CoefficientList[Series[-(x^18 - x^17 + 2 x^16 - 15 x^15 + 17 x^14 - 236 x^13 + 253 x^12 - 2007 x^11 + 2260 x^10 - 4267 x^9 - 2260 x^8 - 2007 x^7 - 253 x^6 - 236 x^5 - 17 x^4 - 15 x^3 - 2 x^2 - x - 1)/((x^10 - 502 x^5 - 1) (x^10 + 502 x^5 - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 21 2013 *)
PROG
(Magma) I:=[1, 1, 2, 15, 17, 236, 253, 2007, 2260, 4267, 249746, 254013, 503759, 3780326, 4284085, 59473431, 63757516, 505776043, 569533559, 1075309602]; [n le 20 select I[n] else 252006*Self(n-10)-Self(n-20): n in [1..70]]; // Vincenzo Librandi, Dec 21 2013
CROSSREFS
Sequence in context: A041797 A041289 A249944 * A031022 A194542 A076646
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Dec 21 2013
STATUS
approved