A160721 First differences of A160720.

1, 4, 4, 12, 4, 12, 12, 28, 4, 12, 12, 28, 12, 28, 28, 60, 4, 12, 12, 28, 12, 28, 28, 60, 12, 28, 28, 60, 28, 60, 60, 124, 4, 12, 12, 28, 12, 28, 28, 60, 12, 28, 28, 60, 28, 60, 60, 124, 12, 28, 28, 60, 28, 60, 60, 124, 28, 60, 60, 124, 60, 124, 124, 252, 4, 12, 12, 28, 12, 28, 28

Offset: 1

Author

Omar E. Pol, May 25 2009, May 29 2009

Keywords

• nonn
• tabf

Comments

This sequence is related to the Sierpinski triangle and to Gould's sequence A001316. - Omar E. Pol, Jul 23 2009

When written as a irregular triangle in which row lengths are A011782 it appears that right border gives A173033. - Omar E. Pol, Mar 20 2013

Examples

			From _Omar E. Pol_, Mar 20 2013 (Start):
Triangle begins:
1;
4;
4,12;
4,12,12,28;
4,12,12,28,12,28,28,60;
4,12,12,28,12,28,28,60,12,28,28,60,28,60,60,124;
4,12,12,28,12,28,28,60,12,28,28,60,28,60,60,124,12,28,28,60,28,60,60,124,28,60,60,124,60,124,124,252;
(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.]
• David Applegate, The movie version
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A000120, A001316, A038573, A139250, A139251, A160720, A160722, A160723.

Formula

a(1)=1. Observation: It appears that a(n) = 4*A038573(n-1), n>1. [From Omar E. Pol, Jul 23 2009]. This formula is correct! - N. J. A. Sloane, Jan 23 2016

Extensions

More terms from R. J. Mathar, Jul 14 2009