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

Author

N. J. A. Sloane, Jan 26 2001

Keywords

• tabf
• easy
• nonn

Comments

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

Examples

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

References

• 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.

Links

• 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

Crossrefs

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

Extensions

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