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A050037 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) = a(2) = 1 and a(3) = 4.

%I A050037 #16 Nov 08 2019 16:51:18
%S A050037 1,1,4,5,6,11,15,16,17,33,48,59,65,70,74,75,76,151,225,295,360,419,
%T A050037 467,500,517,533,548,559,565,570,574,575,576,1151,1725,2295,2860,3419,
%U A050037 3967,4500,5017,5517,5984,6403,6763,7058,7283,7434
%N A050037 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) = a(2) = 1 and a(3) = 4.
%H A050037 Ivan Neretin, <a href="/A050037/b050037.txt">Table of n, a(n) for n = 1..8193</a>
%p A050037 a := proc(n) option remember;
%p A050037 `if`(n < 4, [1, 1, 4][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;
%p A050037 seq(a(n), n = 1 .. 48); # _Petros Hadjicostas_, Nov 08 2019
%t A050037 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 4}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* _Ivan Neretin_, Sep 07 2015 *)
%Y A050037 Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050061 (1,3,2), A050065 (1,3,3), A050069 (1,3,4).
%K A050037 nonn
%O A050037 1,3
%A A050037 _Clark Kimberling_
%E A050037 Name edited by _Petros Hadjicostas_, Nov 08 2019