OFFSET
0,1
COMMENTS
The three levels are:{1,2,3},{4,5,6},{7,8,9} They give triangular states as: {1} :as 0th state {4, 5, 4}, {8, 9, 8}, {2, 3, 2, 3, 1, 3, 2, 3, 2}, {5, 6, 5, 6, 4, 6, 5, 6, 5, 6, 4, 6, 4, 5, 4, 6, 4, 6, 5, 6, 5, 6, 4, 6, 5, 6,5}, {9, 7, 8, 9, 9, 7, 8, 9, 8, 7, 8, 9, 9, 7, 8, 9, 9, 7, 8, 9, 8, 7, 8, 9, 8, 9, 8, 7, 8, 9, 8, 7, 8, 9, 9, 7, 8, 9, 9, 7, 8, 9, 8, 7, 8, 9, 9, 7, 8, 9, 9},
LINKS
F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 96, section 4.11.
FORMULA
1->{4, 5, 6}, 2->{5, 6, 5}, 3->{6, 4, 6}, 4->{8}, 5->{9}, 6->{7, 8, 9}, 7->{1, 2, 1}, 8->{2, 3, 2}, 9->{3, 1, 3}
MATHEMATICA
s[1] = {4, 5, 4}; s[2] = {5, 6, 5}; s[3] = {6, 4, 6}; s[4] = {8}; s[5] = {9}; s[6] = {7, 8, 9}; s[7] = {1, 2, 1}; s[8] = {2, 3, 2}; s[9] = {3, 1, 3}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = Table[p[i], {i, 1, 6}] Flatten[aa]
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, May 07 2005
STATUS
approved