A050060 - OEIS

%I #21 Nov 15 2019 03:30:13

%S 1,3,2,3,5,6,8,13,21,22,24,29,37,58,82,119,201,202,204,209,217,238,

%T 262,299,381,582,786,1003,1265,1646,2432,3697,6129,6130,6132,6137,

%U 6145,6166,6190,6227,6309,6510,6714,6931,7193,7574,8360

%N a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3, and a(3) = 2.

%C Variant of A050028 and A050044. - _R. J. Mathar_, Oct 15 2008

%H Ivan Neretin, <a href="/A050060/b050060.txt">Table of n, a(n) for n = 1..8193</a>

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

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

%p end proc:

%p seq(a(n), n = 1..60); # _Petros Hadjicostas_, Nov 14 2019

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

%Y Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050064 (1,3,3), A050068 (1,3,4).

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Nov 14 2019