Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Sep 26 2019 01:54:24
%S 1,3,4,11,30,52,112,265,743,1224,2456,4953,10119,21197,46123,108490,
%T 304273,500059,1000126,2000293,4000799,8002557,16008843,32033930,
%U 64155153,128701875,258903984,523810232,1071651837,2239971619
%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), with a(1) = 1, a(2) = 3, and a(3) = 4.
%F a(n) = a(1 + A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4 with a(1) = 1, a(2) = 3, and a(3) = 4. - _Petros Hadjicostas_, Sep 24 2019
%e From _Petros Hadjicostas_, Sep 24 2019: (Start)
%e a(4) = a(1 + A006257(4-2)) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 3 + 1 + 3 + 4 = 11.
%e a(7) = a(1 + A006257(7-2)) + a(1) + ... + a(6) = a(4) + a(1) + ... + a(6) = 11 + 1 + 3 + 4 + 11 + 30 + 52 = 112.
%e (End)
%p a := proc(n) local i; option remember; if n < 4 then return [1, 3, 4][n]; end if; add(a(i), i = 1 .. n - 1) + a(2*n - 3 - Bits:-Iff(n - 2, n - 2)); end proc;
%p seq(a(n), n = 1 .. 37); # _Petros Hadjicostas_, Sep 24 2019, courtesy of _Peter Luschny_
%Y Cf. A006257, A049939, A049940, A049960, A049964.
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Sep 24 2019