A123479 - OEIS

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A123479

Coefficients of series giving the best rational approximations to sqrt(6).

20, 1980, 194040, 19013960, 1863174060, 182572043940, 17890197132080, 1753056746899920, 171781670999060100, 16832850701160989900, 1649447587042777950120, 161629030679491078121880 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`The partial sums of the series 5/2 - 1/a(1) - 1/a(2) - 1/a(3) - ... give the best rational approximations to sqrt(6), which constitute every second convergent of the continued fraction. The corresponding continued fractions are [2;2], [2;2,4,2], [2;2,4,2,4,2], [2;2,4,2,4,2,4,2] and so forth.`
	FORMULA	`a(n+3) = 99 a(n+2) - 99 a(n+1) + a(n) a(n) = -5/24 + (5/48+1/246^(1/2))(49+206^(1/2))^n + (5/48-1/246^(1/2))(49-206^(1/2))^n`
	CROSSREFS	`Cf. A123478, A123480, A029549, A123482.` `Sequence in context: A014606 A172556 A072818 * A071152 A195622 A064878` `Adjacent sequences: A123476 A123477 A123478 * A123480 A123481 A123482`
	KEYWORD	`nonn`
	AUTHOR	`Gene Ward Smith (genewardsmith(AT)gmail.com), Sep 28 2006`

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Last modified February 14 23:53 EST 2012. Contains 205689 sequences.