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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 and a(2) = a(3) = 3.
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%I #10 Apr 26 2020 02:19:44

%S 1,3,3,8,18,34,70,140,285,563,1128,2256,4517,9044,18104,36244,72558,

%T 144977,289956,579912,1159829,2319668,4639352,9278740,18557550,

%U 37115245,74230768,148462101,296925330,593852921,1187710369,2375429798

%N 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 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(-1 + log[2](n - 1)) + n - 1)):

%p end proc:

%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Apr 25 2020

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Apr 25 2020