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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) = a(2) = a(3) = 1.
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%I #23 May 06 2022 13:12:16

%S 1,1,1,4,11,19,41,97,272,448,899,1813,3704,7759,16883,39712,111377,

%T 183043,366089,732193,1464464,2929279,5859923,11725792,23483537,

%U 47110405,94769960,191737006,392270525,819925663,1784477927,4197144511

%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) = a(2) = a(3) = 1.

%F a(n) = (1/2)*A049959(n) for n > 3. - _Petros Hadjicostas_, Apr 27 2020

%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, 1, 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_, Apr 25 2020

%Y Cf. A049886 (similar, but with minus a(m/2)), A049887 (similar, but with minus a(m)), A049934 (similar, but with plus a(m)), A049959.

%K nonn

%O 1,4

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Apr 25 2020