A187564 - OEIS

A187564

Differences between the Gullwing sequence A187220 and A147562 (Ulam-Warburton cellular automaton).

1, 2, 2, 6, 2, 6, 10, 22, 2, 6, 10, 22, 10, 30, 50, 78, 2, 6, 10, 22, 10, 30, 50, 78, 10, 30, 50, 86, 58, 142, 210, 262, 2, 6, 10, 22, 10, 30, 50, 78, 10, 30, 50, 86, 58, 142, 210, 262, 10, 30

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OFFSET

1,2

COMMENTS

Apparently the Gullwing sequence A187220 is the connection between the Ulam-Warburton C. A. (A147562) and the toothpick sequence A139250.

Note that the more complex structure is A187220, followed by A139250 and then A147562.

For another version with minimal differences but asynchronous see A187223.

LINKS

Table of n, a(n) for n=1..50.

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

FORMULA

a(n) = A187220(n) - A147562(n-1).

EXAMPLE

If written as a triangle begins:

2,6,

2,6,10,22,

2,6,10,22,10,30,50,78,

2,6,10,22,10,30,50,78,10,30,50,86,58,142,210,262,

2,6,10,22,10,30,50,78,10,30,50,86,58,142,210,262,10,30...

CROSSREFS

Cf. A139250, A147562, A187220, A187223.