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a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = 2*n - 2 - 2^(p+1) 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.
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%I #10 Nov 20 2019 01:41:32

%S 1,1,4,5,6,16,28,45,61,166,328,645,1261,2401,4323,6890,9291,25471,

%T 50938,101865,203701,407281,814083,1626410,3248331,6478081,12879768,

%U 25454120,49689111,94526551,170077063,271081695,365608246,1002298186

%N a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = 2*n - 2 - 2^(p+1) 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.

%p s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:

%p a := proc(n) option remember;

%p `if`(n < 4, [1, 1, 4][n], s(n - 1) - a(-2^ceil(log[2](n - 1)) + 2*n - 2)):

%p end proc:

%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 19 2019

%K nonn

%O 1,3

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Nov 19 2019