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a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) 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) = 3.
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%I #10 Nov 16 2019 03:28:59

%S 1,3,3,8,18,34,70,155,362,655,1312,2639,5330,10952,22854,49726,116976,

%T 211099,422200,844415,1688882,3378056,6757062,13518142,27053808,

%U 54201738,108708700,218684082,442436344,905169434,1891993760

%N a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) 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) = 3.

%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, 3, 3][n], s(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):

%p end proc:

%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 15 2019

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Nov 15 2019