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%I #13 Nov 20 2019 09:45:15
%S 1,2,1,2,4,8,16,26,34,92,184,362,706,1346,2422,3860,5206,14270,28540,
%T 57074,114130,228194,456118,911252,1819990,3629570,7216336,14261552,
%U 27840046,52961774,95291566,151882910,204844684,561572276
%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) = 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 - 2)):
%p end proc:
%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 20 2019
%o (PARI) lista(nn) = {my(va = vector(nn), s); va[1] = 1; va[2] = 2; va[3] = 1; s = sum(k=1, 3, va[k]); for (n=4, nn, va[n] = s - va[2*n - 2 - 2^ceil(log(n-1)/log(2))]; s += va[n]; ); va; } \\ _Petros Hadjicostas_, Nov 20 2019 by modifying a program of _Michel Marcus_
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Nov 20 2019