A049941 - OEIS

%I #23 Oct 26 2019 02:15:54

%S 1,1,3,6,12,29,55,108,216,539,1025,2024,4031,8056,16109,32216,64432,

%T 161079,306051,604049,1204073,2406139,4811279,9622072,19243821,

%U 38487534,76975015,153950004,307899991,615799976,1231599949,2463199896,4926399792,12315999479,23400399011

%N a(n) = a(1) + a(2) + ... + a(n-1) + a(m), 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.

%F From _Petros Hadjicostas_, Oct 06 2019: (Start)

%F a(n) = a(2 - n + 2^ceiling(log_2(n-1))) + Sum_{i = 1..n-1} a(i) for n >= 3.

%F a(n) = a(n - 1 - A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 3.

%F (End)

%e From _Petros Hadjicostas_, Oct 06 2019: (Start)

%e a(3) = a(2 - 3 + 2^ceiling(log_2(3-1))) + a(1) + a(2) = a(1) + a(1) + a(2) = 3.

%e a(4) = a(2 - 4 + 2^ceiling(log_2(4-1))) + a(1) + a(2) + a(3) =  a(2) + a(1) + a(2) + a(3) = 6.

%e a(5) = a(5 - 1 - A006257(5-2)) + a(1) + a(2) + a(3) + a(4) = a(1) + a(1) + a(2) + a(3) + a(4) = 12.

%e (End)

%p a := proc(n) local i; option remember; if n < 3 then return [1, 1][n]; end if; add(a(i), i = 1 .. n - 1) + a(3 - n + Bits:-Iff(n - 2, n - 2)); end proc;

%p seq(a(n), n = 1 .. 35); # _Petros Hadjicostas_, Oct 06 2019

%Y Cf. A006257.

%K nonn

%O 1,3

%A _Clark Kimberling_

%E More terms from _Petros Hadjicostas_, Oct 06 2019