The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Feb 27 2018 04:05:54
%S 1,2,3,10,12,14,16,19,22,26,30,33,37,39,43,45,48,51,53,56,59,61,65,67,
%T 70,73,76,79,82,85,88,91,95,97,101,104,107,111,113,117,120,123,126,
%U 129,132,135,139,141,145,147,151,153,157,159,163,165,169,171
%N a(n) = c(n-1) + c(n-3) where c is the sequence of numbers not in a.
%H Ivan Neretin, <a href="/A022427/b022427.txt">Table of n, a(n) for n = 0..10000</a>
%H J-P. Bode, H. Harborth, C. Kimberling, <a href="https://www.fq.math.ca/Papers1/45-3/bode.pdf">Complementary Fibonacci sequences</a>, Fibonacci Quarterly 45 (2007), 254-264.
%t Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 2}]]] &, {1, 2, 3}, Range[55]] (* _Ivan Neretin_, Mar 28 2017 *)
%Y Cf. A022424 and references therein.
%Y Cf. A299536.
%K nonn
%O 0,2
%A _Clark Kimberling_