A050057 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) = 3, and a(3) = 1.

1, 3, 1, 4, 5, 9, 10, 13, 14, 27, 37, 46, 51, 55, 56, 59, 60, 119, 175, 230, 281, 327, 364, 391, 405, 418, 428, 437, 442, 446, 447, 450, 451, 901, 1348, 1794, 2236, 2673, 3101, 3519, 3924, 4315, 4679, 5006, 5287, 5517, 5692, 5811

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), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050061 (1,3,2), A050065 (1,3,3), A050069 (1,3,4).

Programs

Maple

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

Mathematica

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 1}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 08 2015 *)

Extensions

Name edited by Petros Hadjicostas, Nov 08 2019