A050033 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.

1, 1, 3, 4, 5, 9, 12, 13, 14, 27, 39, 48, 53, 57, 60, 61, 62, 123, 183, 240, 293, 341, 380, 407, 421, 434, 446, 455, 460, 464, 467, 468, 469, 937, 1404, 1868, 2328, 2783, 3229, 3663, 4084, 4491, 4871, 5212, 5505, 5745, 5928, 6051

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8193

Crossrefs

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).

Programs

Maple

a := proc(n) option remember;
`if`(n < 4, [1, 1, 3][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;
seq(a(n), n = 1 .. 48); # Petros Hadjicostas, Nov 08 2019

Mathematica

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 *)

Extensions

Name edited by Petros Hadjicostas, Nov 08 2019