A050056 - OEIS

%I #15 Nov 16 2019 01:40:12

%S 1,3,1,2,3,4,5,8,13,14,15,18,23,36,51,74,125,126,127,130,135,148,163,

%T 186,237,362,489,624,787,1024,1513,2300,3813,3814,3815,3818,3823,3836,

%U 3851,3874,3925,4050,4177,4312,4475,4712,5201

%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) = 1.

%H Ivan Neretin, <a href="/A050056/b050056.txt">Table of n, a(n) for n = 1..8193</a>

%p a := proc(n) option remember; `if`(n < 4, [1, 3, 1][n],

%p        a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):

%p      end proc:

%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 15 2019

%t Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 1}, 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), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Nov 15 2019