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A041101
Denominators of continued fraction convergents to sqrt(58).
2
1, 1, 2, 3, 5, 8, 13, 190, 203, 393, 596, 989, 1585, 2574, 37621, 40195, 77816, 118011, 195827, 313838, 509665, 7449148, 7958813, 15407961, 23366774, 38774735, 62141509, 100916244, 1474968925, 1575885169, 3050854094, 4626739263, 7677593357, 12304332620
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,198,0,0,0,0,0,0,1).
FORMULA
G.f.: -(x^12 -x^11 +2*x^10 -3*x^9 +5*x^8 -8*x^7 +13*x^6 +8*x^5 +5*x^4 +3*x^3 +2*x^2 +x +1) / (x^14 +198*x^7 -1). - Colin Barker, Nov 12 2013
a(n) = 198*a(n-7) + a(n-14). - Vincenzo Librandi, Dec 11 2013
MATHEMATICA
Denominator[Convergents[Sqrt[58], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
PROG
(Magma) I:=[1, 1, 2, 3, 5, 8, 13, 190, 203, 393, 596, 989, 1585, 2574]; [n le 14 select I[n] else 198*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 12 2013
STATUS
approved