1,1

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.

a(n+3) = 399 a(n+2) - 399 a(n+1) + a(n); a(n) = -5/33 + (5/66+1/44*11^(1/2))*(199+60*11^(1/2))^n + (5/66-1/44*11^(1/2))*(199-60*11^(1/2))^n

Cf. A123478, A123479, A123480, A029549.

Sequence in context: A001460 A003794 A068295 this_sequence A092870 A003788 A123378

Adjacent sequences: A123479 A123480 A123481 this_sequence A123483 A123484 A123485

nonn

Gene Ward Smith (genewardsmith(AT)gmail.com), Oct 02 2006