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%I #12 Apr 24 2020 02:10:26
%S 1,2,1,6,16,28,60,142,398,656,1316,2654,5422,11358,24714,58132,163038,
%T 267946,535896,1071814,2143742,4287998,8577994,17164692,34376158,
%U 68962130,138728128,280672440,574221574,1200240586,2612191482
%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), 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; `if`(n < 4, [1, 2, 1][n], s(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 2)); end proc;
%p seq(a(n), n = 1 .. 40); # _Petros Hadjicostas_, Apr 23 2020
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Apr 23 2020