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 A267700 "Tree" sequence in a 90 degree sector of the cellular automaton of A160720. 7
 0, 1, 2, 5, 6, 9, 12, 19, 20, 23, 26, 33, 36, 43, 50, 65, 66, 69, 72, 79, 82, 89, 96, 111, 114, 121, 128, 143, 150, 165, 180, 211, 212, 215, 218, 225, 228, 235, 242, 257, 260, 267, 274, 289, 296, 311, 326, 357, 360, 367, 374, 389, 396, 411, 426, 457, 464, 479, 494, 525, 540, 571, 602, 665, 666, 669, 672, 679, 682, 689 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjecture: this is also the "tree" sequence in a 120 degree sector of the cellular automaton of A266532. It appears that this is also the partial sums of A038573. a(n) is also the total number of ON cells after n-th stage in the tree that arises from one of the four spokes in a 90 degree sector of the cellular automaton A160720 on the square grid. Note that the structure of A160720 is also the "outward" version of the Ulam-Warburton cellular automaton of A147562. It appears that A038573 gives the number of cells turned ON at n-th stage. Conjecture: a(n) is also the total number of Y-toothpicks after n-th stage in the tree that arises from one of the three spokes in a 120 degree sector of the cellular automaton of A266532 on the triangular grid. Note that the structure of A266532 is also the "outward" version of the Y-toothpick cellular automaton of A160120. It appears that A038573 also gives the number of Y-toothpicks added at n-th stage. Comment from N. J. A. Sloane, Jan 23 2016: All the above conjectures are true! LINKS David Applegate, The movie version N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA a(n) = (A160720(n+1) - 1)/4. Conjecture 1: a(n) = (A266532(n+1) - 1)/3. Conjecture 2: a(n) = A160720(n+1) - A266532(n+1). All of the above conjectures are true -  N. J. A. Sloane, Jan 23 2016 CROSSREFS Cf. A000120, A038573, A147562, A160120, A160720, A161336, A169779, A266532, A266534, A266536. Sequence in context: A050487 A046962 A022486 * A161910 A151920 A160714 Adjacent sequences:  A267697 A267698 A267699 * A267701 A267702 A267703 KEYWORD nonn AUTHOR Omar E. Pol, Jan 19 2016 STATUS approved

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Last modified December 12 19:25 EST 2018. Contains 318081 sequences. (Running on oeis4.)