A079315 Number of cells that change from OFF to ON at stage n of the cellular automaton described in A079317.

0, 1, 4, 4, 12, 4, 20, 12, 44, 4, 52, 12, 76, 12, 100, 36, 172, 4, 180, 12, 204, 12, 228, 36, 300, 12, 324, 36, 396, 36, 468, 108, 684, 4, 692, 12, 716, 12, 740, 36, 812, 12, 836, 36, 908, 36, 980, 108, 1196, 12, 1220, 36, 1292, 36, 1364, 108, 1580, 36, 1652, 108, 1868

Offset

0,3

Comments

Start with cell (0,0) ON; at each succeeding stage the cells that share exactly one edge with an active cell change their state.

This is not the CA discussed by Singmaster in the reference given in A079314. That was an error based on my misreading of the paper. - N. J. A. Sloane, Aug 05 2009

References

D. Singmaster, On the cellular automaton of Ulam and Warburton, M500 Magazine of the Open University, #195 (December 2003), pp. 2-7.

Links

Table of n, a(n) for n=0..60.

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.]

D. Singmaster, On the cellular automaton of Ulam and Warburton, 2003 [Cached copy, included with permission]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Formula

a(2n+1) = A147582(n+1), a(2n) = A151914(n).

Mathematica

wt[n_] := DigitCount[n, 2, 1];
A147582[n_] := If[n == 1, 1, 4*3^(wt[n-1]-1)];
A151914[n_] := Switch[n, 0, 0, 1, 4, _, (8/3)*Sum[3^wt[i], {i, 1, n-1}]+4];
a[n_] := If[OddQ[n], A147582[(n-1)/2+1], A151914[n/2]];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Apr 21 2024 *)

Crossrefs

Cf. A079316-A079319, A147582, A151914, A151917, A151920, A151921, A139250.

Sequence in context: A328854 A253064 A109045 * A229253 A272789 A273152

Adjacent sequences: A079312 A079313 A079314 * A079316 A079317 A079318

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Feb 12 2003

Extensions

More terms from John W. Layman, Oct 30 2003

Edited by N. J. A. Sloane, Aug 05 2009

Status

approved