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A049902 a(n) = a(1) + a(2) + ... + 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) = 1.

%I A049902 #10 Nov 20 2019 01:41:36
%S A049902 1,2,1,3,5,11,21,43,84,170,339,679,1356,2710,5414,10818,21614,43270,
%T A049902 86539,173079,346156,692310,1384614,2769218,5538414,11076787,22153488,
%U A049902 44306807,88613274,177225871,354450388,708898072,1417790740
%N A049902 a(n) = a(1) + a(2) + ... + 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) = 1.
%p A049902 s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:
%p A049902 a := proc(n) option remember;
%p A049902 `if`(n < 4, [1, 2, 1][n], s(n - 1) - a(-2^ceil(-1 + log[2](n - 1)) + n - 1)):
%p A049902 end proc:
%p A049902 seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 19 2019
%K A049902 nonn
%O A049902 1,2
%A A049902 _Clark Kimberling_
%E A049902 Name edited by _Petros Hadjicostas_, Nov 19 2019