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%I #10 Nov 17 2019 01:56:04
%S 1,3,4,9,21,39,81,179,418,756,1515,3047,6154,12645,26387,57413,135059,
%T 243732,487467,974951,1949962,3900261,7801619,15607877,31235987,
%U 62580646,125513700,252489895,510831447,1045097262,2184472237
%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) = 3, 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, 3, 4][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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