A050056 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, a(2) = 3, and a(3) = 1.

1, 3, 1, 2, 3, 4, 5, 8, 13, 14, 15, 18, 23, 36, 51, 74, 125, 126, 127, 130, 135, 148, 163, 186, 237, 362, 489, 624, 787, 1024, 1513, 2300, 3813, 3814, 3815, 3818, 3823, 3836, 3851, 3874, 3925, 4050, 4177, 4312, 4475, 4712, 5201

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, 3, 1][n],
       a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
     end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 15 2019

Mathematica

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 1}, 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), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

Sequence in context: A135564 A110063 A260313 * A209882 A336233 A325845

Adjacent sequences: A050053 A050054 A050055 * A050057 A050058 A050059

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Nov 15 2019

Status

approved