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%I #10 Apr 26 2020 02:20:10
%S 1,1,4,7,20,34,74,175,491,808,1622,3271,6683,13999,30461,71650,200951,
%T 330253,660512,1321051,2642243,5285119,10572701,21156130,42369911,
%U 84998425,170987648,345939364,707749739,1479341773,3219624485
%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_, Apr 25 2020
%K nonn
%O 1,3
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Apr 25 2020