cp's OEIS Frontend

A050054 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, a(2) = 2, and a(3) = 4.

%I A050054 #15 Nov 19 2019 05:51:31
%S A050054 1,2,4,5,7,8,10,14,19,20,22,26,31,38,46,56,70,71,73,77,82,89,97,107,
%T A050054 121,140,160,182,208,239,277,323,379,380,382,386,391,398,406,416,430,
%U A050054 449,469,491,517,548,586,632
%N A050054 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, a(2) = 2, and a(3) = 4.
%H A050054 Ivan Neretin, <a href="/A050054/b050054.txt">Table of n, a(n) for n = 1..8193</a>
%p A050054 a := proc(n) option remember;
%p A050054      `if`(n < 4, [1, 2, 4][n], a(n - 1) + a(-2^ceil(-1+log[2](n - 1)) + n - 1)):
%p A050054      end proc:
%p A050054 seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 18 2019
%t A050054 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 4}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 08 2015 *)
%Y A050054 Cf. similar sequences with different initial conditions listed in A050034.
%K A050054 nonn
%O A050054 1,2
%A A050054 _Clark Kimberling_
%E A050054 Name edited by _Petros Hadjicostas_, Nov 18 2019