1,1

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.

a(n+3) = 99 a(n+2) - 99 a(n+1) + a(n) a(n) = -5/24 + (5/48+1/24*6^(1/2))*(49+20*6^(1/2))^n + (5/48-1/24*6^(1/2))*(49-20*6^(1/2))^n

Cf. A123478, A123480, A029549, A123482.

Sequence in context: A094035 A014606 A072818 this_sequence A071152 A064878 A145405

Adjacent sequences: A123476 A123477 A123478 this_sequence A123480 A123481 A123482

nonn

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