A050053 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) = 4.

1, 2, 4, 6, 7, 13, 17, 19, 20, 39, 56, 69, 76, 82, 86, 88, 89, 177, 263, 345, 421, 490, 546, 585, 605, 624, 641, 654, 661, 667, 671, 673, 674, 1347, 2018, 2685, 3346, 4000, 4641, 5265, 5870, 6455, 7001, 7491, 7912, 8257, 8520, 8697

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), 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, 4][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;
seq(a(n), n = 1 .. 48); # Petros Hadjicostas, Nov 09 2019

Mathematica

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 4}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 08 2015 *)

Extensions

Name edited by Petros Hadjicostas, Nov 09 2019