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A042266
Numerators of continued fraction convergents to sqrt(659).
2
25, 26, 77, 1951, 3979, 5930, 300479, 306409, 913297, 23138834, 47190965, 70329799, 3563680915, 3634010714, 10831702343, 274426569289, 559684840921, 834111410210, 42265255351421, 43099366761631
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 11860, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (25 + 26*x + 77*x^2 + 1951*x^3 + 3979*x^4 + 5930*x^5 + 3979*x^6 - 1951*x^7 + 77*x^8 - 26*x^9 + 25*x^10 - x^11)/(1 - 11860*x^6 + x^12). - Vincenzo Librandi, Nov 20 2013
a(n) = 11860*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 18 2013
MATHEMATICA
Numerator[Convergents[Sqrt[659], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 77 x^2 + 1951 x^3 + 3979 x^4 + 5930 x^5 + 3979 x^6 - 1951 x^7 + 77 x^8 - 26 x^9 + 25 x^10 - x^11)/(1 - 11860 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 11860, 0, 0, 0, 0, 0, -1}, {25, 26, 77, 1951, 3979, 5930, 300479, 306409, 913297, 23138834, 47190965, 70329799}, 30] (* Harvey P. Dale, Jan 04 2023 *)
PROG
(Magma) I:=[25, 26, 77, 1951, 3979, 5930, 300479, 306409, 913297, 23138834, 47190965, 70329799]; [n le 12 select I[n] else 11860*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013
CROSSREFS
Cf. A042267.
Sequence in context: A042274 A042270 A042268 * A042278 A042276 A042282
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved