0,2

All terms are distinct, but the numbers 2^m - 1 are missing.

a(n)=sum(k>=1,B(n+k-1,k)*2^(A103586(n)-k)) where B(n,k) n>=1, k>=1 is the infinite array:

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

.......

where n-th row consists of binary expansion of n followed by 0's.

David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

0

1

1 0

1 1

1 0 0

1 0 1

1 1 0

1 1 1

1 0 0 0

1 0 0 1

1 0 1 0

and reading the diagonals downwards we get 0, 10, 110, 101, 100, 1110, 1101, etc.

Cf. A102370, A105030, A105025-A105028, A105033.

Adjacent sequences: A105026 A105027 A105028 this_sequence A105030 A105031 A105032

Sequence in context: A118138 A004583 A021381 this_sequence A067548 A053793 A076187

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 03 2005