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A050065 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n 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 A050065 #14 Nov 08 2019 16:51:38
%S A050065 1,3,3,6,7,13,16,19,20,39,55,68,75,81,84,87,88,175,259,340,415,483,
%T A050065 538,577,597,616,632,645,652,658,661,664,665,1329,1990,2648,3300,3945,
%U A050065 4577,5193,5790,6367,6905,7388,7803,8143,8402,8577
%N A050065 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n 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 A050065 Ivan Neretin, <a href="/A050065/b050065.txt">Table of n, a(n) for n = 1..8193</a>
%p A050065 a := proc(n) option remember;
%p A050065 `if`(n < 4, [1, 3, 3][n], a(n - 1) + a(Bits:-Iff(n - 2, n - 2) + 3 - n)); end proc;
%p A050065 seq(a(n), n = 1 .. 48); # _Petros Hadjicostas_, Nov 08 2019
%t A050065 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 3}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* _Ivan Neretin_, Sep 08 2015 *)
%Y A050065 Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050037 (1,1,4), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050061 (1,3,2), A050069 (1,3,4).
%K A050065 nonn
%O A050065 1,2
%A A050065 _Clark Kimberling_
%E A050065 Name edited by _Petros Hadjicostas_, Nov 08 2019