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Given the infinite continued fraction (1+i)+((1+i)/(1+i)+((1+i)/((1+i)+...)))), where i is the square root of (-1), this is the numerator of the imaginary part of the convergents.
2

%I #2 Mar 30 2012 17:31:00

%S 1,1,4,3,11,97,280,101,2337,2251,19516,14101,163009,16245,30256,

%T 245929,11371969,32865601,94983348,22875581,19349753,2292794785,

%U 6626299912,2393795271,2635503517,159951677089,462268926316,11517086141

%N Given the infinite continued fraction (1+i)+((1+i)/(1+i)+((1+i)/((1+i)+...)))), where i is the square root of (-1), this is the numerator of the imaginary part of the convergents.

%t Table[ Im[ Numerator[ FromContinuedFraction[ Table[1 + I, {n}]]]], {n, 30}]

%Y Cf. A091806, A091807, A091808, A091809, A093725, A093727.

%K frac,nonn

%O 1,3

%A _Robert G. Wilson v_, Mar 11 2004