The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261180 Flowsnake phases, exp(I 2 Pi a(n) / 6) are vectors in a sequence that visits points of the hexagonal root lattice A_2. 5
 0, 1, 3, 2, 0, 0, 5, 0, 1, 1, 3, 4, 2, 1, 2, 3, 3, 5, 0, 4, 3, 2, 3, 5, 4, 2, 2, 1, 0, 1, 3, 2, 0, 0, 5, 0, 1, 3, 2, 0, 0, 5, 4, 5, 5, 1, 2, 0, 5, 0, 1, 3, 2, 0, 0, 5, 0, 1, 1, 3, 4, 2, 1, 0, 1, 1, 3, 4, 2, 1, 2, 3, 3, 5, 0, 4, 3, 4, 5, 1, 0, 4, 4, 3, 2, 3, 5, 4, 2, 2, 1, 0, 1, 1, 3, 4, 2, 1, 2, 3, 5, 4, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This sequence is generated by a Lindenmayer system over six symbols, { M[n], P[n] } with n in {0,1,2}. The replacement rules are: P[n] |---> P[n], M[n - 1], M[n], P[n + 1], P[n], P[n], M[n + 1]; M[n] |---> P[n + 1], M[n], M[n], M[n + 1], P[n], P[n - 1], M[n]; with all arithmetic evaluated modulo 3. The numeric sequence changes the signed vectors M[n] and P[n] into exponent coefficients according to another set of replacement rules: P[n] |---> Mod[2 n, 6]; M[n] |---> Mod[2 n + 3, 6]. The axiom for sequence is P[0]=0; however, other axioms are just as good. a(n) is one of three right infinite sequences. The other right infinite sequences are a(3*7+n) and a(11*7+n). If n is a negative number, the left infinite sequences are (a(-n)+3) mod 6, (a(-3*7-n)+3) mod 6, and (a(-11*7-n)+3) mod 6. The valid two-way infinite sequences are generated from M[n]|P[m], n != m, or: { 1|0, 5|0, 1|2, 3|2, 3|4, 5|4 }. LINKS J. H. Conway, Chaim Goodman-Strauss, and N. J. A. Sloane, Recent progress in sphere packing, Current Developments in Mathematics, (1999) 37-76. Martin Gardner, Mathematical Games: In which "monster" curves force redefinition of the word "curve", Scientific American, volume 235, number 6, December 1976, pages 124-133. Martin Gardner, Penrose Tiles to Trapdoor Ciphers: And the Return of Dr Matrix, Mathematical Association of America, 1996, chapter 3 (revised and expanded reprint of Mathematical Games article). Bradley Klee, A Pit of Flowsnakes, Complex Systems, 24, 4 (2015), section 2. MATHEMATICA FLSN = {P[n_] :> {P[n], M[n - 1], M[n], P[n + 1], P[n], P[n], M[n + 1]}, M[n_] :> {P[n + 1], M[n], M[n], M[n + 1], P[n], P[n - 1], M[n]}}; a[1]=P[0]; Map[(a[n_/; IntegerQ[(n - #)/7]]:=Part[Flatten[a[(n + 7 - #)/7] /. FLSN], #]) &, Range[7]]; Mod[a /@ Range[7*7]/.{P[x_]:>Mod[2 x, 6], M[x_]:>Mod[2 x + 3, 6]}, 6] CROSSREFS Cf. A229214 (as +-1,2,3), A261185 (mod 2), A261120. Coordinates: A334485, A334486. Sequence in context: A322114 A062787 A131370 * A062707 A160230 A293500 Adjacent sequences:  A261177 A261178 A261179 * A261181 A261182 A261183 KEYWORD nonn AUTHOR Bradley Klee, Aug 10 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 12 01:36 EDT 2021. Contains 342912 sequences. (Running on oeis4.)