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A041251
Denominators of continued fraction convergents to sqrt(137).
2
1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712, 11799905, 12319617, 36439139, 85197895, 121637034, 206834929, 535306892, 1277448713, 1812755605, 41158072023, 42970827628, 127099727279, 297170282186
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,3488,0,0,0,0,0,0,0,0,1).
FORMULA
G.f.: -(x^16 -x^15 +3*x^14 -7*x^13 +10*x^12 -17*x^11 +44*x^10 -105*x^9 +149*x^8 +105*x^7 +44*x^6 +17*x^5 +10*x^4 +7*x^3 +3*x^2 +x +1) / (x^18 +3488*x^9 -1). - Colin Barker, Nov 14 2013
a(n) = 3488*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 13 2013
MATHEMATICA
Denominator[Convergents[Sqrt[137], 30]] (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 3488, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712}, 40] (* Harvey P. Dale, Oct 29 2022 *)
PROG
(Magma) I:=[1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712]; [n le 18 select I[n] else 3488*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013
CROSSREFS
Sequence in context: A304216 A305247 A316547 * A042435 A042591 A098001
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved