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A042626 revision #9

A042626

Numerators of continued fraction convergents to sqrt(843).

29, 842, 48865, 1417927, 82288631, 2387788226, 138574005739, 4021033954657, 233358543375845, 6771418791854162, 392975648470917241, 11403065224448454151, 661770758666481257999, 19202755066552404936122

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index to sequences with linear recurrences with constant coefficients, signature (0,1684,0,-1).

FORMULA

G.f.: (29 +842*x +29*x^2 -x^3)/(1 -1684*x^2 +x^4). - Vincenzo Librandi, Nov 30 2013

a(n) = 1684*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 30 2013

MATHEMATICA

Numerator[Convergents[Sqrt[843], 30]] (* or *) CoefficientList[Series[(29 + 842 x + 29 x^2 - x^3)/(1 - 1684 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 30 2013 *)

PROG

(MAGMA) I:=[29, 842, 48865, 1417927]; [n le 4 select I[n] else 1684*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013

CROSSREFS

Cf. A042627.

Sequence in context: A278475 A057687 A049667 * A157877 A158665 A324432

Adjacent sequences: A042623 A042624 A042625 * A042627 A042628 A042629

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

editing