A050066 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p 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, 4, 7, 8, 11, 14, 18, 19, 22, 25, 29, 36, 44, 55, 69, 70, 73, 76, 80, 87, 95, 106, 120, 138, 157, 179, 204, 233, 269, 313, 368, 369, 372, 375, 379, 386, 394, 405, 419, 437, 456, 478, 503, 532, 568, 612

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 listed in A050034.

Programs

Maple

a := proc(n) option remember;
     `if`(n < 4, [1, 3, 3][n], a(n - 1) + a(-2^ceil(-1+log[2](n - 1)) + n - 1)):
     end proc:
seq(a(n), n = 1..40); #

Mathematica

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

Extensions

Name edited by Petros Hadjicostas, Nov 18 2019