A094266 LQTL Lean Quaternary Temporal Logic: a terse form of temporal logic created by assigning four descriptors such that false, becoming true, true and becoming false are represented and become a linear sequence. In a branching tree two alternative are open, change or no change. The integer sequence above is the count of the row possibilities of the four states over successive iterations.

1, 1, 0, 0, 1, 2, 1, 0, 1, 3, 3, 1, 2, 4, 6, 4, 6, 6, 10, 10, 16, 12, 16, 20, 36, 28, 28, 36, 72, 64, 56, 64, 136, 136, 120, 120, 256, 272, 256, 240, 496, 528, 528, 496, 992, 1024, 1056, 1024, 2016, 2016, 2080, 2080, 4096, 4032, 4096, 4160, 8256, 8128, 8128, 8256, 16512

Offset: 0

Author

Robert H Barbour and L. D. Painter, Jun 01 2004

Keywords

• easy
• nonn

Comments

This is a table read by rows of length 4. Every row is formed from the previous one by the circular Pascal triangle-like rule: a, b, c, d -> d+a, a+b, b+c, c+d. Consider a labeled binary tree such that the root has label 0 and every node labeled k has children labeled k and (k+1) mod 4; the n-th row of this sequence counts nodes on the level n+1 with labels 0, 1, 2, 3, while the n-th row of A099423 counts nodes up to level n. - Andrey Zabolotskiy, Jan 06 2023

Links

• Robert H. Barbour, 2D Four-Color Cellular Automaton, NKS 2006 Wolfram Science Conference.
• Robert H. Barbour, Two-dimensional Four Color Cellular Automaton: Surface Explorations, Complex Systems, 17 (2007), 103-112.

Crossrefs

Cf. A000749, A005418, A038503, A038504, A038505, A020522, A063376.

Programs

Maple

Algorithm available from Robert H Barbour

Formula

Appears to satisfy a 12-degree linear recurrence. - Ralf Stephan, Dec 04 2004