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%I #26 Nov 07 2019 18:32:05
%S 1,1,4,7,14,34,65,127,254,634,1206,2381,4742,9477,18951,37899,75798,
%T 189494,360040,710606,1416477,2830593,5660011,11319450,22638520,
%U 45276913,90553764,181107497,362214974,724429941,1448859879,2897719755,5795439510,14488598774,27528337672,54332245406
%N a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n-1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 4.
%F From _Petros Hadjicostas_, Nov 06 2019: (Start)
%F a(n) = a(2^ceiling(log_2(n-1)) + 2 - n) + Sum_{i = 1..n-1} a(i) for n >= 4.
%F a(n) = a(n - 1 - A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4. (End)
%e From _Petros Hadjicostas_, Nov 06 2019: (Start)
%e a(4) = a(2^ceiling(log_2(4-1)) + 2 - 4) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 7.
%e a(5) = a(2^ceiling(log_2(5-1)) + 2 - 5) + a(1) + a(2) + a(3) + a(4) = a(1) + a(1) + a(2) + a(3) + a(4) = 14.
%e a(6) = a(2^ceiling(log_2(6-1)) + 2 - 6) + a(1) + a(2) + a(3) + a(4) + a(5) = a(4) + a(1) + a(2) + a(3) + a(4) + a(5) = 34.
%e a(7) = a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = a(3) + Sum_{i = 1..6} a(i) = 65.
%e a(8) = a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = a(2) + Sum_{i = 1..7} a(i) = 127. (End)
%p s:= proc(n) option remember; `if`(n<1, 0, a(n)+s(n-1)) end:
%p a:= proc(n) option remember; `if`(n<4, [1, 1, 4][n],
%p s(n-1)+a(Bits:-Iff(n-2$2)+3-n))
%p end:
%p seq(a(n), n=1..36); # _Petros Hadjicostas_, Nov 06 2019
%Y Cf. A006257, A049933, A049937.
%K nonn
%O 1,3
%A _Clark Kimberling_
%E Name edited by and more terms from _Petros Hadjicostas_, Nov 06 2019
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