A123480 - OEIS

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A123480

Coefficients of the series giving the best rational approximations to sqrt(3).

4, 60, 840, 11704, 163020, 2270580, 31625104, 440480880, 6135107220, 85451020204, 1190179175640, 16577057438760, 230888624967004, 3215863692099300, 44791203064423200, 623860979209825504 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`The partial sums of the series 2 - 1/a(1) - 1/a(2) - 1/a(3) - ... give the best rational approximations to sqrt(3), which constitute every second convergent of the continued fraction. The corresponding continued fractions are [1;1,2,1], [1;1,2,1,2,1], [1;1,2,1,2,1,2,1], [1;1,2,1,2,1,2,1,2,1] and so forth.`
	FORMULA	`a(n+3) = 15 a(n+2) - 15 a(n+1) + a(n) a(n) = -1/3 + (1/6+1/123^(1/2))(7+43^(1/2))^n + (1/6-1/123^(1/2))(7-43^(1/2))^n`
	CROSSREFS	`Cf. A123478, A123479, A029549, A123482.` `Sequence in context: A034866 A055315 A013482 * A156090 A181418 A013486` `Adjacent sequences: A123477 A123478 A123479 * A123481 A123482 A123483`
	KEYWORD	`nonn`
	AUTHOR	`Gene Ward Smith (genewardsmith(AT)gmail.com), Sep 28 2006`

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Last modified February 14 18:09 EST 2012. Contains 205663 sequences.