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A187223

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

0, 0, 2, 2, 6, 2, 6, 2, 14, 2, 6, 2, 14, 2, 6, -14, 30, 2, 6, 2, 14, 2, 6, -14, 30, 2, 6, -14, 22, -22, -34, -102, 62, 2, 6, 2, 14, 2, 6, -14, 30, 2, 6, -14, 22, -22, -34, -102, 62, 2, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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 which contains only positive terms and is more synchronous see the triangle A187564.

LINKS

Table of n, a(n) for n=0..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) = A147562(n) - A187220(n).

EXAMPLE

Contribution from Omar E. Pol, Aug 25 2012 (Start):

Written as a triangle the sequence begins:

2,6,

2,6,2,14,

2,6,2,14,2,6,-14,30,

2,6,2,14,2,6,-14,30,2,6,-14,22,-22,-34,-102,62,

2,6,2,14,2,6,-14,30,2,6,-14,22,-22,-34,-102,62,2,6,...

(End)