1,1

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.

a(n+3) = 15 a(n+2) - 15 a(n+1) + a(n) a(n) = -1/3 + (1/6+1/12*3^(1/2))*(7+4*3^(1/2))^n + (1/6-1/12*3^(1/2))*(7-4*3^(1/2))^n

Cf. A123478, A123479, A029549, A123482.

Sequence in context: A034866 A055315 A013482 this_sequence A156090 A013486 A013483

Adjacent sequences: A123477 A123478 A123479 this_sequence A123481 A123482 A123483

nonn

Gene Ward Smith (genewardsmith(AT)gmail.com), Sep 28 2006