A323110 - OEIS

%I #22 Feb 10 2019 17:26:53

%S 1,5,9,21,9,45,57,213,129,645,1161,2709,657,3285,5841,13869,3129,

%T 15645,28161,65709,28161,140805,178353,666477,391137,1955685,3520233,

%U 8213877,3518721,17593605,22290273,83271357,48828129,244140645,439453161,1025390709,439453161,2197265805,2783203353,10400391477

%N Aggregate values of n-th stage of growth for two-dimensional cellular automaton defined by "Rule 614", based on the 5-celled von Neumann neighborhood, calculated via even-zeroing instead of mod 2.

%C It's helpful to define A072272 first: Consider only the four nearest (N,S,E,W) neighbors of a cell together with the cell itself. In the next state, the state of a cell will change if an odd number of these five cells is ON. This is equivalent to taking the sum of all 4 neighbor cells, together with the cell itself, mod 2. A072272 is the total number of active cells per generation. This sequence differs from A072272 because the state of the next cell can be any odd number instead of 1. Instead of applying mod 2 to the sum of the 5 local cells, this variation takes the sum of the 5 local cells, and then sets the value to zero if that value is even.

%C The generations of A072272 are congruent mod 2 to the generations of this automaton. A consequence of this is that the pattern of active cells is the same between both implementations of the CA. However, the values of the cells in this automaton differ from those in A072272. In this variation the values of cell are not constrained to the range [0,1]. The terms in this sequence are the aggregate values of all cells for each generation, instead of the number of cells.

%H Nathan Epstein, <a href="https://giant.gfycat.com/GlassSlipperyEider.webm">Animation of CA generating A323110</a>

%Y Cf. A072272.

%K nonn

%O 0,2

%A _Nathan M Epstein_, Jan 04 2019