Puzzles/Easy Sequence 2/Solution

Add 1 2 3 4... OR x(x-1)/2+1 :

1 2 4 7 11 16 22 29 ...

$$a_n = a_{n-2} + a_{n-1} + 1$$:

1 2 4 7 12 20 33 ...

Add the three previous numbers:

1 2 4 7 13 24 44 ...

The numbers with an odd number of ones in their binary representation:

1 2 4 7 8 11 13 ... or 1 10 100 111 1000 1011 1101 ...

A formula for the $$n$$th number is: $$a_0 = 1$$, $$a_{2n} = a_n + 2n$$, $$a_{2n+1} = 6n + 3 - a_n $$.