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

Author

Clark Kimberling

Keywords

• nonn

Links

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

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).

Programs

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 *)

Extensions

Name edited by Petros Hadjicostas, Nov 14 2019