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A050046 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) = 2.

%I A050046 #16 Apr 24 2020 02:11:17
%S A050046 1,2,2,3,5,6,8,10,13,14,16,18,21,26,32,40,50,51,53,55,58,63,69,77,87,
%T A050046 100,114,130,148,169,195,227,267,268,270,272,275,280,286,294,304,317,
%U A050046 331,347,365,386,412,444
%N A050046 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) = 2.
%H A050046 Ivan Neretin, <a href="/A050046/b050046.txt">Table of n, a(n) for n = 1..8193</a>
%p A050046 a := proc(n) option remember;
%p A050046      `if`(n < 4, [1, 2, 2][n], a(n - 1) + a(-2^ceil(-1+log[2](n - 1)) + n - 1)):
%p A050046      end proc:
%p A050046 seq(a(n), n = 1..40); # _Petros Hadjicostas_, Apr 23 2020
%t A050046 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 2}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 08 2015 *)
%Y A050046 Cf. similar sequences listed in A050034.
%K A050046 nonn
%O A050046 1,2
%A A050046 _Clark Kimberling_
%E A050046 Name edited by _Petros Hadjicostas_, Apr 23 2020