A022800 a(n) = F(n+2) + c(n) where F(k) is k-th Fibonacci number and c(n) is n-th number that is 1 or is a non-Fibonacci number.

3, 7, 11, 15, 22, 31, 45, 67, 103, 159, 249, 394, 628, 1006, 1617, 2606, 4204, 6789, 10971, 17737, 28684, 46396, 75054, 121423, 196449, 317843, 514262, 832075, 1346305, 2178346, 3524616, 5702926, 9227505