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

1,2

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

Links

Table of n, a(n) for n=1..71.

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

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

Example

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)

Crossrefs

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

Sequence in context: A273391 A273452 A178182 * A151836 A147582 A162793

Adjacent sequences: A160718 A160719 A160720 * A160722 A160723 A160724

Keyword

nonn,tabf

Author

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

Extensions

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

Status

approved