A050041 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) = 1, a(2) = 2, and a(3) = 1.

1, 2, 1, 3, 4, 7, 8, 10, 11, 21, 29, 36, 40, 43, 44, 46, 47, 93, 137, 180, 220, 256, 285, 306, 317, 327, 335, 342, 346, 349, 350, 352, 353, 705, 1055, 1404, 1750, 2092, 2427, 2754, 3071, 3377, 3662, 3918, 4138, 4318, 4455, 4548, 4595

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), A050033 (1,1,3), A050037 (1,1,4), 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, 2, 1][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;
seq(a(n), n = 1..50); # Petros Hadjicostas, Nov 11 2019

Mathematica

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 1}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 07 2015 *)

Extensions

Name edited by Petros Hadjicostas, Nov 11 2019