A079315 - OEIS

%I #19 Apr 21 2024 11:40:31

%S 0,1,4,4,12,4,20,12,44,4,52,12,76,12,100,36,172,4,180,12,204,12,228,

%T 36,300,12,324,36,396,36,468,108,684,4,692,12,716,12,740,36,812,12,

%U 836,36,908,36,980,108,1196,12,1220,36,1292,36,1364,108,1580,36,1652,108,1868

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

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

%C 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

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

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]

%H D. Singmaster, <a href="/A079314/a079314.pdf">On the cellular automaton of Ulam and Warburton</a>, 2003 [Cached copy, included with permission]

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

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

%t wt[n_] := DigitCount[n, 2, 1];

%t A147582[n_] := If[n == 1, 1, 4*3^(wt[n-1]-1)];

%t A151914[n_] := Switch[n, 0, 0, 1, 4, _, (8/3)*Sum[3^wt[i], {i, 1, n-1}]+4];

%t a[n_] := If[OddQ[n], A147582[(n-1)/2+1], A151914[n/2]];

%t Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Apr 21 2024 *)

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

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Feb 12 2003

%E More terms from _John W. Layman_, Oct 30 2003

%E Edited by _N. J. A. Sloane_, Aug 05 2009