ContinuedFraction[3^(1/4),  500];

Count[%1, 1]

Count[%1, 2]

Count[%1, 3]

Partition[%1, 2];

Delete[%1, 1];

Partition[%6, 2];

Count[%7, {1, 1}] + Count[%5,  {1, 1}]