0,3

It appears that the sums of two successive terms give the positive terms of the toothpick sequence A139250.

It appears that the odd terms (a bisection) give A162795.

It appears that a(n) is also the total number of ON cells at stage n+1 in one of the four wedges of two-dimensional cellular automaton "Rule 750" using the von Neumann neighborhood (see A169707). Therefore a(n) is also the total number of ON cells at stage n+1 in one of the four quadrants of the NW-NE-SE-SW version of that cellular automaton.

See also the formula section.

First differs from A169779 at a(11).

Ivan Neretin, Table of n, a(n) for n = 0..8191

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191 arXiv:1004.3036

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

It appears that a(n) + a(n-1) = A139250(n), n >= 1.

It appears that a(2n-1) = A162795(n), n >= 1.

It appears that a(n) = (A169707(n+1) - 1)/4.

Also, written as an irregular triangle in which the row lengths are the terms of A011782 (the number of compositions of n, n >= 0), the sequence begins:

0;

1;

2, 5;

6, 9, 14, 21;

22, 25, 30, 37, 42, 53, 70, 85;

86, 89, 94,101,106,117,134,149,154,165,182,201,222,261,310,341;

...

It appears that the first column gives 0 together with the terms of A047849, hence the right border gives A002450.

It appears that this triangle only shares with A151920 the positive elements of the columns 1, 2, 4, 8, 16, ... (the powers of 2).

Accumulate[Nest[Join[#, 2 # + Append[Rest@#, 1]] &, {0}, 6]] (* Ivan Neretin, Feb 09 2017 *)

Cf. A002450, A011782, A047849, A139250, A151548, A151920, A160552, A162795, A169707, A169779, A246336.

Sequence in context: A163782 A362140 A226793 * A256264 A256249 A169779

Adjacent sequences: A255744 A255745 A255746 * A255748 A255749 A255750

Omar E. Pol, Mar 05 2015

approved