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%I #9 Nov 16 2019 00:52:00
%S 1,1,2,3,5,11,21,39,62,144,287,571,1126,2211,4197,7555,12039,28274,
%T 56547,113091,226166,452291,904357,1807875,3612679,7217516,14390524,
%U 28611429,56544667,110381012,209984179,377814215,602188918
%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) = a(2) = 1 and a(3) = 2.
%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, 2][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 1,3
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Nov 15 2019
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