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: a₀ = 1, a_2n = a_n + 2n, a_{2n + 1} = 6n + 3 − a_n.