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A041949
Denominators of continued fraction convergents to sqrt(497).
2
1, 3, 7, 17, 92, 569, 2937, 6443, 15823, 53912, 2387951, 7217765, 16823481, 40864727, 221147116, 1367747423, 7059884231, 15487515885, 38034916001, 129592263888, 5740094527073, 17349875845107, 40439846217287, 98229568279681, 531587687615692
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 2403774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^18 -3*x^17 +7*x^16 -17*x^15 +92*x^14 -569*x^13 +2937*x^12 -6443*x^11 +15823*x^10 -53912*x^9 -15823*x^8 -6443*x^7 -2937*x^6 -569*x^5 -92*x^4 -17*x^3 -7*x^2 -3*x -1) / (x^20 -2403774*x^10 +1). - Colin Barker, Nov 27 2013
a(n) = 2403774*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 27 2013
MATHEMATICA
Denominator[Convergents[Sqrt[497], 30]] (* Vincenzo Librandi, Dec 27 2013 *)
PROG
(Magma) I:=[1, 3, 7, 17, 92, 569, 2937, 6443, 15823, 53912, 2387951, 7217765, 16823481, 40864727, 221147116, 1367747423, 7059884231, 15487515885, 38034916001, 129592263888]; [n le 20 select I[n] else 2403774*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013
CROSSREFS
Sequence in context: A246764 A128343 A106877 * A222452 A218165 A102329
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 27 2013
STATUS
approved