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A042493
Denominators of continued fraction convergents to sqrt(774).
2
1, 1, 5, 6, 11, 28, 39, 67, 307, 374, 20503, 20877, 104011, 124888, 228899, 582686, 811585, 1394271, 6388669, 7782940, 426667429, 434450369, 2164468905, 2598919274, 4763388179, 12125695632, 16889083811, 29014779443, 132948201583, 161962981026, 8878949176987
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 20810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^18 -x^17 +5*x^16 -6*x^15 +11*x^14 -28*x^13 +39*x^12 -67*x^11 +307*x^10 -374*x^9 -307*x^8 -67*x^7 -39*x^6 -28*x^5 -11*x^4 -6*x^3 -5*x^2 -x -1) / (x^20 -20810*x^10 +1). - Colin Barker, Dec 15 2013
a(n) = 20810*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 15 2013
MATHEMATICA
Denominator[Convergents[Sqrt[774], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 20810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 5, 6, 11, 28, 39, 67, 307, 374, 20503, 20877, 104011, 124888, 228899, 582686, 811585, 1394271, 6388669, 7782940, 426667429}, 40] (* Harvey P. Dale, Jun 29 2015 *)
PROG
(Magma) I:=[1, 1, 5, 6, 11, 28, 39, 67, 307, 374, 20503, 20877, 104011, 124888, 228899, 582686, 811585, 1394271, 6388669, 7782940]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013
CROSSREFS
Sequence in context: A046828 A328095 A046830 * A042217 A041355 A041050
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Dec 15 2013
STATUS
approved