A123482 - OEIS

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A123482

Coefficients of the series giving the best rational approximations to sqrt(11).

60, 23940, 9528120, 3792167880, 1509273288180, 600686976527820, 239071907384784240, 95150018452167599760, 37869468272055319920300, 15071953222259565160679700, 5998599512991034878630600360 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`The partial sums of the series 10/3 - 1/a(1) - 1/a(2) - 1/a(3) - ... give the best rational approximations to sqrt(11), which constitute every second convergent of the continued fraction. The corresponding continued fractions are [3;3,6,3], [3;3,6,3,6,3], [3;3,6,3,6,3,6,3] and so forth.`
	FORMULA	`a(n+3) = 399 a(n+2) - 399 a(n+1) + a(n); a(n) = -5/33 + (5/66+1/4411^(1/2))(199+6011^(1/2))^n + (5/66-1/4411^(1/2))(199-6011^(1/2))^n`
	CROSSREFS	`Cf. A123478, A123479, A123480, A029549.` `Sequence in context: A003794 A068295 A177643 * A092870 A185560 A003788` `Adjacent sequences: A123479 A123480 A123481 * A123483 A123484 A123485`
	KEYWORD	`nonn`
	AUTHOR	`Gene Ward Smith (genewardsmith(AT)gmail.com), Oct 02 2006`

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Last modified February 16 21:51 EST 2012. Contains 205978 sequences.