A050030 - OEIS

A050030

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

%I #14 May 10 2020 23:13:34

%S 1,1,2,3,4,5,6,8,11,12,13,15,18,22,27,33,41,42,43,45,48,52,57,63,71,

%T 82,94,107,122,140,162,189,222,223,224,226,229,233,238,244,252,263,

%U 275,288,303,321,343,370,403

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

%H Ivan Neretin, <a href="/A050030/b050030.txt">Table of n, a(n) for n = 1..8193</a>

%t Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1}, Flatten@Table[k, {n, 0, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 06 2015 *)

%o (PARI) lista(nn) = {nn = max(nn, 2); my(va = vector(nn)); va[1] = 1; va[2] = 1; for(n=3, nn, va[n] = va[n-1] + va[n - 1 - 2^logint(n-2, 2)]); va; } \\ _Petros Hadjicostas_, May 10 2020

%K nonn

%O 1,3

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, May 10 2020