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%I #10 Nov 16 2019 03:27:44
%S 1,2,1,5,10,20,40,89,208,377,754,1517,3064,6296,13138,28586,67246,
%T 121355,242710,485429,970888,1941944,3884434,7771178,15552430,
%U 31158968,62493400,125714978,254343502,520355000,1087650970,2367152042
%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, a(2) = 2, and a(3) = 1.
%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, 2, 1][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
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