A050034 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) = a(2) = 1 and a(3) = 3.

1, 1, 3, 4, 5, 6, 7, 10, 14, 15, 16, 19, 23, 28, 34, 41, 51, 52, 53, 56, 60, 65, 71, 78, 88, 102, 117, 133, 152, 175, 203, 237, 278, 279, 280, 283, 287, 292, 298, 305, 315, 329, 344, 360, 379, 402, 430, 464

Offset

1,3

Links

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

Mathematica

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 3}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

Prog

(PARI) lista(nn) = {nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 3; for(n=4, nn, va[n] = va[n-1] + va[n - 1 - 2^logint(n-2, 2)]); va; } \\ Petros Hadjicostas, May 10 2020

Crossrefs

Cf. similar sequences with different initial conditions: A050026 (1,1,1); A050030 (1,1,2); this sequence (1,1,3); A050038 (1,1,4); A050042 (1,2,1); A050046 (1,2,2); A050050 (1,2,3); A050054 (1,2,4); A050058 (1,3,1); A050062 (1,3,2); A050066 (1,3,3); A050070 (1,3,4).

Sequence in context: A087190 A085038 A163078 * A039056 A326754 A047562

Adjacent sequences: A050031 A050032 A050033 * A050035 A050036 A050037

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, May 10 2020

Status

approved