A050029 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) = 2.

1, 1, 2, 3, 4, 7, 9, 10, 11, 21, 30, 37, 41, 44, 46, 47, 48, 95, 141, 185, 226, 263, 293, 314, 325, 335, 344, 351, 355, 358, 360, 361, 362, 723, 1083, 1441, 1796, 2147, 2491, 2826, 3151, 3465, 3758, 4021, 4247, 4432, 4573, 4668, 4716

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A006257, A050025 (similar, but with different initial conditions).

Programs

Maple

a := proc(n) option remember;
`if`(n < 4, [1, 1, 2][n], a(n - 1) + a(Bits:-Iff((n - 2) $ 2) + 3 - n));
end proc;
seq(a(n), n = 1 .. 50); # Petros Hadjicostas, Nov 07 2019

Mathematica

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

Formula

From Petros Hadjicostas, Nov 08 2019: (Start)

a(n) = a(2^ceiling(log_2(n-1)) + 2 - n) + a(n-1) for n >= 4.

a(n) = a(n - 1 - A006257(n-2)) + a(n-1) for n >= 4. (End)

Extensions

Name edited by Petros Hadjicostas, Nov 07 2019