A079316 Number of first-quadrant cells (including the two boundaries) that are ON at stage n of the cellular automaton described in A079317.

1, 3, 3, 7, 5, 11, 9, 21, 11, 25, 15, 35, 19, 45, 29, 73, 31, 77, 35, 87, 39, 97, 49, 125, 53, 135, 63, 163, 73, 191, 101, 273, 103, 277, 107, 287, 111, 297, 121, 325, 125, 335, 135, 363, 145, 391, 173, 473, 177, 483, 187, 511, 197, 539, 225, 621, 235, 649, 263, 731

Offset: 0

Author

N. J. A. Sloane, Feb 12 2003

Keywords

• nonn
• easy

Comments

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

The pattern has 4-fold symmetry; sequence just counts cells in one quadrant.

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

• 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

Crossrefs

Cf. A079317, A151922, A151923.

Programs

PARI

M=matrix(101,101); M[1,1]=1; for(s=1,100, c=[]; a=M[1,1]; for(x=2,100, for(y=2,100, a+=M[x,y]; if(M[x-1,y]+M[x+1,y]+M[x,y-1]+M[x,y+1]==1, c=concat(c,[[x,y]]) )); a+=M[x,1]+M[1,x]; if(M[x,2]==0 && M[x-1,1]+M[x+1,1]==1, c=concat(c,[[x,1]]) ); if(M[2,x]==0 && M[1,x-1]+M[1,x+1]==1, c=concat(c,[[1,x]]) )); print1(a,", "); for(i=1,length(c),M[c[i][1],c[i][2]]=1-M[c[i][1],c[i][2]]) ) \\ Max Alekseyev, Feb 02 2007

Extensions

More terms from Max Alekseyev, Feb 02 2007

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