A023491 a(n) = b(n) + d(n), where b(n) = (n-th Fibonacci number > 1) and d(n) = (n-th non-Lucas number).
4, 8, 11, 16, 22, 31, 46, 68, 103, 159, 249, 394, 629, 1007, 1618, 2606, 4204, 6789, 10971, 17737, 28684, 46396, 75055, 121424, 196450, 317844, 514263, 832075, 1346305, 2178346, 3524616, 5702926, 9227505, 14930393, 24157859, 39088212, 63246030, 102334200
Offset: 0
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Corrected by Clark Kimberling, Jan 29 2019