A050032 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique value such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 3.

1, 1, 3, 4, 7, 8, 11, 18, 29, 30, 33, 40, 51, 80, 113, 164, 277, 278, 281, 288, 299, 328, 361, 412, 525, 802, 1083, 1382, 1743, 2268, 3351, 5094, 8445, 8446, 8449, 8456, 8467, 8496, 8529, 8580, 8693, 8970, 9251, 9550, 9911, 10436

Offset

1,3

Links

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

Maple

a := proc(n) option remember;
`if`(n < 4, [1, 1, 3][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, 1, 3}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Crossrefs

Similar sequences with different initial conditions are A050024 (1,1,1), A050028 (1,1,2), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), 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: A196923 A192051 A033195 * A330221 A343151 A014602

Adjacent sequences: A050029 A050030 A050031 * A050033 A050034 A050035

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Nov 14 2019

Status

approved