A050028 - OEIS

%I #18 May 10 2020 22:59:53

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

%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) = a(2) = 1 and a(3) = 2.

%H Ivan Neretin, <a href="/A050028/b050028.txt">Table of n, a(n) for n = 1..8193</a>

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

%p       if n < 4 then return [1, 1, 2][n]; end if;

%p       a(n - 1) + a(2*n - 4 - Bits:-Iff(n - 2, n - 2)); end proc;

%p seq(a(n), n = 1 .. 50); # _Petros Hadjicostas_, Nov 08 2019

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

%o (PARI) lista(nn) = {nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 2; for(n=4, nn, va[n] = va[n-1] + va[2*n - 3 - 2*2^logint(n-2, 2)]); va; } \\ _Petros Hadjicostas_, May 10 2020

%Y Cf. A050024 (similar, but with different initial conditions).

%K nonn

%O 1,3

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Nov 08 2019