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%I #30 May 06 2022 13:12:16
%S 1,1,3,6,12,24,48,98,199,393,786,1574,3151,6308,12628,25280,50610,
%T 101123,202246,404494,808991,1617988,3235988,6472000,12944050,
%U 25888201,51776596,103553585,207107958,414217493,828438143,1656882606,3313777864,6627530449,13255060898,26510121798,53020243599
%N a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 3, 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) = a(2) = 1.
%H Petros Hadjicostas, <a href="/A049942/b049942.txt">Table of n, a(n) for n = 1..3323</a>
%F From _Petros Hadjicostas_, Oct 25 2019: (Start)
%F a(n) = a(n - 1 - 2^ceiling(-1 + log_2(n-1))) + Sum_{i = 1..n-1} a(i) for n >= 3.
%F a(n) = a((1 + A006257(n-2))/2) + Sum_{i = 1..n-1} a(i) for n >= 3.
%F (End)
%e From _Petros Hadjicostas_, Oct 25 2019: (Start)
%e a(3) = a(3 - 1 - 2^ceiling(-1 + log_2(3-1))) + a(1) + a(2) = a(1) + a(1) + a(2) = 3.
%e a(4) = a(4 - 1 - 2^ceiling(-1 + log_2(4-1))) + a(1) + a(2) + a(3) = a(1) + a(1) + a(2) + a(3) = 6.
%e a(5) = a(5 - 1 - 2^ceiling(-1 + log_2(5-1))) + a(1) + a(2) + a(3) + a(4) = a(2) + a(1) + a(2) + a(3) + a(4) = 12.
%e a(6) = a(6 - 1 - 2^ceiling(-1 + log_2(6-1))) + a(1) + a(2) + a(3) + a(4) + a(5) = a(1) + a(1) + a(2) + a(3) + a(4) + a(5) = 24.
%e (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<3, 1, s(n-1)+
%p a(n-3/2-1/2*Bits:-Iff(n-2, n-2)))
%p end:
%p seq(a(n), n=1..50); # _Petros Hadjicostas_, Oct 25 2019
%Y Cf. A006257, A049894 (similar, but with minus a(m)), A049895 (similar, but with minus a(2*m)), A049943 (similar, but with plus a(2*m)).
%K nonn
%O 1,3
%A _Clark Kimberling_
%E More terms from _Petros Hadjicostas_, Oct 25 2019
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