A023490 a(n) = b(n) + d(n), where b(n) = ( (n+1)st Fibonacci number) and d(n) = (n-th nonLucas number).

3, 7, 9, 13, 17, 23, 33, 47, 69, 104, 160, 250, 396, 630, 1008, 1619, 2607, 4205, 6790, 10972, 17738, 28685, 46397, 75055, 121424, 196450, 317844, 514263, 832075, 1346305, 2178346, 3524616, 5702926, 9227505, 14930393, 24157859