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A049979 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. 2

%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

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)