A050045 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n 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, 4, 5, 9, 11, 13, 14, 27, 38, 47, 52, 56, 58, 60, 61, 121, 179, 235, 287, 334, 372, 399, 413, 426, 437, 446, 451, 455, 457, 459, 460, 919, 1376, 1831, 2282, 2728, 3165, 3591, 4004, 4403, 4775, 5109, 5396, 5631, 5810, 5931

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)):
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[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 07 2015 *)

Crossrefs

Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050037 (1,1,4), A050041 (1,2,1), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050061 (1,3,2), A050065 (1,3,3), A050069 (1,3,4).

Sequence in context: A308906 A337823 A051630 * A308955 A098386 A326447

Adjacent sequences: A050042 A050043 A050044 * A050046 A050047 A050048

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Nov 14 2019

Status

approved