A050065 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 and a(2) = a(3) = 3.

1, 3, 3, 6, 7, 13, 16, 19, 20, 39, 55, 68, 75, 81, 84, 87, 88, 175, 259, 340, 415, 483, 538, 577, 597, 616, 632, 645, 652, 658, 661, 664, 665, 1329, 1990, 2648, 3300, 3945, 4577, 5193, 5790, 6367, 6905, 7388, 7803, 8143, 8402, 8577

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), A050057 (1,3,1), A050061 (1,3,2), A050069 (1,3,4).

Programs

Maple

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

Extensions

Name edited by Petros Hadjicostas, Nov 08 2019