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A041104
Numerators of continued fraction convergents to sqrt(60).
2
7, 8, 23, 31, 457, 488, 1433, 1921, 28327, 30248, 88823, 119071, 1755817, 1874888, 5505593, 7380481, 108832327, 116212808, 341257943, 457470751, 6745848457, 7203319208, 21152486873, 28355806081, 418133772007, 446489578088, 1311112928183, 1757602506271
OFFSET
0,1
COMMENTS
Interspersion of 4 linear recurrences with constant coefficients. - Gerry Martens, Jun 10 2015
FORMULA
G.f.: -(x^7-7*x^6+8*x^5-23*x^4-31*x^3-23*x^2-8*x-7) / ((x^4-8*x^2+1)*(x^4+8*x^2+1)). - Colin Barker, Nov 05 2013
MAPLE
numtheory:-cfrac(sqrt(60), 50, 'con'):
map(numer, con[1..-2]); # Robert Israel, Jun 09 2015
MATHEMATICA
Numerator/@Convergents[Sqrt[60], 30] (* Harvey P. Dale, Apr 26 2011 *)
n0 := LinearRecurrence[{62, -1}, {7, 457}, 10]
n1 := LinearRecurrence[{62, -1}, {8, 488}, 10]
n2 := LinearRecurrence[{62, -1}, {23, 1433}, 10]
n3 := LinearRecurrence[{62, -1}, {31, 1921}, 10]
Flatten[MapIndexed[{n0[[#]], n1[[#]], n2[[#]], n3[[#]]} &, Range[10]]] (* Gerry Martens, Jun 09 2015 *)
LinearRecurrence[{0, 0, 0, 62, 0, 0, 0, -1}, {7, 8, 23, 31, 457, 488, 1433, 1921}, 28] (* Ray Chandler, Aug 03 2015 *)
CROSSREFS
Sequence in context: A042417 A042845 A295337 * A042391 A042023 A041102
KEYWORD
nonn,cofr,frac,easy
EXTENSIONS
More terms from Colin Barker, Nov 05 2013
STATUS
approved