A050069 a(n) = a(n-1) + a(m) for n >= 3, 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 and a(2) = 3.

1, 3, 4, 7, 8, 15, 19, 22, 23, 45, 64, 79, 87, 94, 98, 101, 102, 203, 301, 395, 482, 561, 625, 670, 693, 715, 734, 749, 757, 764, 768, 771, 772, 1543, 2311, 3075, 3832, 4581, 5315, 6030, 6723, 7393, 8018, 8579, 9061, 9456, 9757

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

In the Mathematica program below, the author of the program uses a(1) = 1, a(2) = 3, and a(3) = 4 as initial conditions. This is not necessary. We get the same sequence using only a(1) = 1 and a(2) = 3 as initial conditions. - Petros Hadjicostas, Nov 13 2019

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), A050057 (1,3,1), A050061 (1,3,2), A050065 (1,3,3).

Programs

Maple

a := proc(n) option remember;
`if`(n < 3, [1, 3][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, 4}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 08 2015 *)

Extensions

Name edited by Petros Hadjicostas, Nov 08 2019