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A042040 Numerators of continued fraction convergents to sqrt(544). 2
23, 70, 793, 2449, 113447, 342790, 3884137, 11995201, 555663383, 1678985350, 19024502233, 58752492049, 2721639136487, 8223669901510, 93182008053097, 287769694060801, 13330587934849943, 40279533498610630 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: (23 +70*x +793*x^2 +2449*x^3 +793*x^4 -70*x^5 +23*x^6 -x^7) / ((1 -70*x^2 +x^4)*(1 +70*x^2 +x^4)). - Vincenzo Librandi, Nov 13 2013
a(n) = 4898*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 14 2013
MATHEMATICA
Numerator[Convergents[Sqrt[544], 30]] (* or *) CoefficientList[Series[(23 + 70 x + 793 x^2 + 2449 x^3 + 793 x^4 - 70 x^5 + 23 x^6 - x^7)/(1 - 4898 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 14 2013 *)
LinearRecurrence[{0, 0, 0, 4898, 0, 0, 0, -1}, {23, 70, 793, 2449, 113447, 342790, 3884137, 11995201}, 20] (* Harvey P. Dale, Jul 27 2020 *)
PROG
(Magma) I:=[23, 70, 793, 2449, 113447, 342790, 3884137, 11995201]; [n le 8 select I[n] else 4898*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013
CROSSREFS
Cf. A042041.
Sequence in context: A042034 A042038 A116333 * A073035 A086104 A274050
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved

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Last modified May 26 05:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)