A284209 -id:A284209 - cp's OEIS frontend

A059318 Pascal's "rhombus" (actually a triangle) mod 2, read by rows: each entry is sum modulo 2 of 3 terms above it in previous row and one term above it two rows back.

1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1

Offset: 0

N. J. A. Sloane, Jan 26 2001

Also, the triangle, read by rows, of successive generations in the reversible cellular automaton RCA(3) when started with a single ON cell at generation 0. - Robert Price, Mar 22 2017

			1; 1,1,1; 1,0,0,0,1; 1,1,0,1,0,1,1; ...

Macfarlane, Alan J. "Linear reversible second-order cellular automata and their first-order matrix equivalents." Journal of Physics A: Mathematical and General 37.45 (2004): 10791. See Fig. 4.

J. Goldwasser et al., The density of ones in Pascal's rhombus, Discrete Math., 204 (1999), 231-236.
Paul K. Stockmeyer, The Pascal Rhombus and the Stealth Configuration, arXiv:1504.04404 [math.CO], 2015.
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A059317, A059319, A059320, A007318, A284208, A284209.

More terms from Larry Reeves (larryr(AT)acm.org), Jan 30 2001

A284208 Binary representation of generation n in the reversible cellular automaton RCA(3) when started with a single ON cell at generation 0.

Original entry on oeis.org

1, 111, 10001, 1101011, 101010101, 11100000111, 1000001000001, 110110111011011, 10100000000000101, 1110111011101110111, 100010100010001010001, 11010110000000001101011, 1010101000001000001010101, 111000000000111000000000111, 10000010100010001000101000001

Offset: 0

Robert Price, Mar 22 2017

nonn

			The second generation (starting at 0) of RCA(3) is x...x where "x" is an ON cell and "." is OFF.  Treating this as a binary number yields 10001.  Thus a(2) = 10001.

Robert Price, Table of n, a(n) for n = 0..999
Alan J. Macfarlane, Linear reversible second-order cellular automata and their first-order matrix equivalents, Journal of Physics A: Mathematical and General 37.45 (2004): 10791. See Fig. 3.
Robert Price, Diagram of the first 35 generations
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A059319, A284209.

cp's OEIS Frontend

A059318 Pascal's "rhombus" (actually a triangle) mod 2, read by rows: each entry is sum modulo 2 of 3 terms above it in previous row and one term above it two rows back.

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