A050048 a(n) = a(n-1) + a(m) for n >= 3, 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) = 2.

1, 2, 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

1,2

Comments

In the Mathematica program below, the author of the program uses the initial conditions a(1) = 1, a(2) = 2, and a(3) = 3. This is not necessary. We get the same sequence using the initial conditions a(1) = 1 and a(2) = 2. - Petros Hadjicostas, Nov 14 2019

Links

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

Maple

a := proc(n) option remember;
`if`(n < 3, [1, 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, 3}, 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), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

Sequence in context: A239389 A256219 A078662 * A122456 A186243 A073882

Adjacent sequences: A050045 A050046 A050047 * A050049 A050050 A050051

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Nov 14 2019

Status

approved