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A049917 a(n) = a(1) + a(2) + ... + 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 A049917 #11 Nov 13 2019 01:38:58
%S A049917 1,3,1,2,6,11,23,44,90,137,295,602,1209,2422,4845,9688,19378,29069,
%T A049917 62981,128385,257983,516573,1033453,2067064,4134175,8268396,16536813,
%U A049917 33073638,66147281,132294566,264589133,529178264,1058356530
%N A049917 a(n) = a(1) + a(2) + ... + 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.
%p A049917 s:= proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:
%p A049917 a := proc(n) option remember;
%p A049917 `if`(n < 4, [1, 3, 1][n], s(n - 1) - a(2^ceil(log[2](n - 1)) + 2 - n)):
%p A049917 end proc:
%p A049917 seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 12 2019
%K A049917 nonn
%O A049917 1,2
%A A049917 _Clark Kimberling_
%E A049917 Name edited by _Petros Hadjicostas_, Nov 12 2019