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%I #23 May 06 2022 13:12:16
%S 1,2,4,8,17,33,67,136,276,545,1091,2184,4372,8753,17522,35078,70225,
%T 140315,280631,561264,1122532,2245073,4490162,8980358,17960785,
%U 35921710,71843689,143687924,287376941,574756070,1149516521,2299041811
%N a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p 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) = 4.
%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, 4][n], s(n - 1) + a(-2^ceil(log[2](n - 1) - 1) + n - 1)); end proc;
%p seq(a(n), n = 1 .. 40); # _Petros Hadjicostas_, Apr 23 2020
%o (PARI) lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 2; va[3] = 4; my(sa = vecsum(va)); for (n=4, nn, va[n] = sa + va[n - 1 - 2^ceil(-1 + log(n-1)/log(2))]; sa += va[n]; ); va; } \\ _Petros Hadjicostas_, Apr 26 2020 (with nn > 2).
%Y Cf. A049914 (similar, but with minus a(m)), A049915 (similar, but with minus a(2*m)), A049963 (similar, but with plus a(2*m)).
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Apr 23 2020
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