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A042576
Numerators of continued fraction convergents to sqrt(817).
2
28, 29, 57, 143, 200, 343, 19408, 19751, 39159, 98069, 137228, 235297, 13313860, 13549157, 26863017, 67275191, 94138208, 161413399, 9133288552, 9294701951, 18427990503, 46150682957, 64578673460
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 686, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (28 +29*x +57*x^2 +143*x^3 +200*x^4 +343*x^5 +200*x^6 -143*x^7 +57*x^8 -29*x^9 +28*x^10 -x^11)/(1 -686*x^6 +x^12). - Vincenzo Librandi, Nov 28 2013
a(n) = 686*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 28 2013
MATHEMATICA
Numerator[Convergents[Sqrt[817], 30]] (* or *) CoefficientList[Series[(28 + 29 x + 57 x^2 + 143 x^3 + 200 x^4 + 343 x^5 + 200 x^6 - 143 x^7 + 57 x^8 - 29 x^9 + 28 x^10 - x^11)/(1 - 686 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 686, 0, 0, 0, 0, 0, -1}, {28, 29, 57, 143, 200, 343, 19408, 19751, 39159, 98069, 137228, 235297}, 30] (* Harvey P. Dale, Jan 17 2017 *)
PROG
(Magma) I:=[28, 29, 57, 143, 200, 343, 19408, 19751, 39159, 98069, 137228, 235297]; [n le 12 select I[n] else 686*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 28 2013
CROSSREFS
Cf. A042577.
Sequence in context: A042578 A042582 A042584 * A042574 A042572 A042570
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved