A170903 a(n) = 2*A160552(n)-1.

1, 1, 5, 1, 5, 9, 13, 1, 5, 9, 13, 9, 21, 33, 29, 1, 5, 9, 13, 9, 21, 33, 29, 9, 21, 33, 37, 41, 77, 97, 61, 1, 5, 9, 13, 9, 21, 33, 29, 9, 21, 33, 37, 41, 77, 97, 61, 9, 21, 33, 37, 41, 77, 97, 69, 41, 77, 105, 117, 161, 253, 257, 125, 1, 5, 9, 13, 9, 21, 33, 29, 9, 21, 33, 37, 41, 77

Offset: 1

Author

Gary W. Adamson, Jan 21 2010

Keywords

• nonn

Examples

			When written as a triangle:
1
1, 5;
1, 5, 9, 13;
1, 5, 9, 13, 9, 21, 33, 29;
...
Rows sums are A006516 (this is immediate from the definition).
From _Omar E. Pol_, Feb 17 2015: (Start)
Also, written as an irregular triangle in which the row lengths are the terms of A011782:
1;
1;
5,1;
5,9,13,1;
5,9,13,9,21,33,29,1;
5,9,13,9,21,33,29,9,21,33,37,41,77,97,61,1;
5,9,13,9,21,33,29,9,21,33,37,41,77,97,61,9,21,33,37,41,77,97,69,41,77,105,117,161,253,257,125,1;
Row sums give 1 together with the positive terms of A006516.
It appears that the right border (A000012) gives the smallest difference between A160164 and A169707 in every period.
(End)
		

Links

• 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. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Cf. A006516, A139250, A139251, A160164, A160552, A169707.

Formula

It appears that a(n) = A160164(n) - A169707(n). - Omar E. Pol, Feb 17 2015