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A050057 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, a(2) = 3, and a(3) = 1.

%I A050057 #17 Nov 08 2019 16:51:29
%S A050057 1,3,1,4,5,9,10,13,14,27,37,46,51,55,56,59,60,119,175,230,281,327,364,
%T A050057 391,405,418,428,437,442,446,447,450,451,901,1348,1794,2236,2673,3101,
%U A050057 3519,3924,4315,4679,5006,5287,5517,5692,5811
%N A050057 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, a(2) = 3, and a(3) = 1.
%H A050057 Ivan Neretin, <a href="/A050057/b050057.txt">Table of n, a(n) for n = 1..8193</a>
%p A050057 a := proc(n) option remember;
%p A050057 `if`(n < 4, [1, 3, 1][n], a(n - 1) + a(Bits:-Iff(n - 2, n - 2) + 3 - n)); end proc;
%p A050057 seq(a(n), n = 1..48); # _Petros Hadjicostas_, Nov 08 2019
%t A050057 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 1}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* _Ivan Neretin_, Sep 08 2015 *)
%Y A050057 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), A050061 (1,3,2), A050065 (1,3,3), A050069 (1,3,4).
%K A050057 nonn
%O A050057 1,2
%A A050057 _Clark Kimberling_
%E A050057 Name edited by _Petros Hadjicostas_, Nov 08 2019