A050044 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) 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) = 2.

1, 2, 2, 3, 5, 6, 8, 13, 21, 22, 24, 29, 37, 58, 82, 119, 201, 202, 204, 209, 217, 238, 262, 299, 381, 582, 786, 1003, 1265, 1646, 2432, 3697, 6129, 6130, 6132, 6137, 6145, 6166, 6190, 6227, 6309, 6510, 6714, 6931, 7193, 7574, 8360

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..8193

Maple

a := proc(n) option remember;
`if`(n < 4, [1, 2, 2][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019

Mathematica

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 2}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Crossrefs

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

Sequence in context: A117356 A017819 A274148 * A308924 A307637 A326462

Adjacent sequences: A050041 A050042 A050043 * A050045 A050046 A050047

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Nov 14 2019

Status

approved