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a(n) = c(n-1) + c(n-3) where c is the sequence of numbers not in a.
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%I #6 Mar 29 2017 20:29:24

%S 1,3,4,8,12,15,17,20,23,25,29,32,35,39,41,45,48,51,54,57,59,63,65,69,

%T 71,74,77,80,83,86,89,91,95,97,101,103,107,109,113,116,119,122,125,

%U 128,131,134

%N a(n) = c(n-1) + c(n-3) where c is the sequence of numbers not in a.

%H Ivan Neretin, <a href="/A022432/b022432.txt">Table of n, a(n) for n = 0..10000</a>

%t Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 2}]]] &, {1, 3, 4}, Range[43]] (* _Ivan Neretin_, Mar 29 2017 *)

%Y Cf. A022424 and references therein.

%K nonn

%O 0,2

%A _Clark Kimberling_