1,1

The partial sums of the series 8/3 - 1/a(1) - 1/a(2) - 1/a(3) - ... give the best rational approximations to sqrt(7), which constitute every fourth convergent of the continued fraction. The corresponding continued fractions are [2;1,1,1], [2;1,1,1,4,1,1,1], [2;1,1,1,4,1,1,1,4,1,1,1] and so forth.

a(n+3) = 255 a(n+2) - 255 a(n+1) + a(n) a(n) = -4/21 + (2/21+1/28*7^(1/2))*(127+48*7^(1/2))^n + (2/21-1/28*7^(1/2))*(127-48*7^(1/2))^n

Cf. A123479, A123480, A029549, A123482.

Sequence in context: A114721 A057868 A130417 this_sequence A159425 A159665 A164278

Adjacent sequences: A123475 A123476 A123477 this_sequence A123479 A123480 A123481

nonn

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