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A050066 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 3.

%I A050066 #15 Nov 19 2019 05:51:25
%S A050066 1,3,3,4,7,8,11,14,18,19,22,25,29,36,44,55,69,70,73,76,80,87,95,106,
%T A050066 120,138,157,179,204,233,269,313,368,369,372,375,379,386,394,405,419,
%U A050066 437,456,478,503,532,568,612
%N A050066 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 3.
%H A050066 Ivan Neretin, <a href="/A050066/b050066.txt">Table of n, a(n) for n = 1..8193</a>
%p A050066 a := proc(n) option remember;
%p A050066      `if`(n < 4, [1, 3, 3][n], a(n - 1) + a(-2^ceil(-1+log[2](n - 1)) + n - 1)):
%p A050066      end proc:
%p A050066 seq(a(n), n = 1..40); #
%t A050066 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 3}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 08 2015 *)
%Y A050066 Cf. similar sequences with different initial conditions listed in A050034.
%K A050066 nonn
%O A050066 1,2
%A A050066 _Clark Kimberling_
%E A050066 Name edited by _Petros Hadjicostas_, Nov 18 2019