A050033 - OEIS

%I #18 Jul 19 2020 11:51:04

%S 1,1,3,4,5,9,12,13,14,27,39,48,53,57,60,61,62,123,183,240,293,341,380,

%T 407,421,434,446,455,460,464,467,468,469,937,1404,1868,2328,2783,3229,

%U 3663,4084,4491,4871,5212,5505,5745,5928,6051

%N a(n) = a(n-1) + a(m) for n >= 4, 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 and a(3) = 3.

%H Ivan Neretin, <a href="/A050033/b050033.txt">Table of n, a(n) for n = 1..8193</a>

%p a := proc(n) option remember;

%p `if`(n < 4, [1, 1, 3][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;

%p seq(a(n), n = 1 .. 48); # _Petros Hadjicostas_, Nov 08 2019

%t Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 3}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* _Ivan Neretin_, Sep 07 2015 *)

%Y Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050037 (1,1,4), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050061 (1,3,2), A050065 (1,3,3), A050069 (1,3,4).

%K nonn

%O 1,3

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Nov 08 2019