A050042 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 1.

1, 2, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 20, 25, 32, 40, 41, 43, 44, 46, 50, 55, 62, 70, 80, 91, 104, 118, 134, 154, 179, 211, 212, 214, 215, 217, 221, 226, 233, 241, 251, 262, 275, 289, 305, 325, 350, 382

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. similar sequences, with different initial conditions, listed in A050034.

Programs

Mathematica

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 1}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

PARI

lista(nn) = {nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 2; va[3] = 1; for(n=4, nn, va[n] = va[n-1] + va[n - 1 - 2^logint(n-2, 2)]); va; } \\ Petros Hadjicostas, May 15 2020

Extensions

Name edited by Petros Hadjicostas, May 15 2020