|
|
A105777
|
|
Trajectory of 1 under the morphism 1->{1,2,2,2,1}, 2->{4,3,3,3,4}, 3->{2,1,1,1,2}, 4->{3,4,4,4,3}.
|
|
1
|
|
|
1, 2, 2, 2, 1, 4, 3, 3, 3, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 4, 1, 2, 2, 2, 1, 3, 4, 4, 4, 3, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 4, 4, 4, 3, 1, 2, 2, 2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Edgar-Peano substitution of 4 symbols taken 5 at a time: characteristic polynomial -x^5 + 5*x^3 + 5*x^2 - 25*x.
|
|
LINKS
|
F. M. Dekking, Recurrent sets, Advances in Mathematics, 44 (1982), 78-104.
|
|
MATHEMATICA
|
s[1] = {1, 2, 2, 2, 1}; s[2] = {4, 3, 3, 3, 4}; s[3] = {2, 1, 1, 1, 2}; s[4] = {3, 4, 4, 4, 3}; s[5] = {} t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[3]
|
|
PROG
|
(PARI) {a(n)=local(A); if(n<1, 0, A=[1]; while(length(A)<n, A=concat(vector(length(A), k, [1, 2, 2, 2, 1; 4, 3, 3, 3, 4; 2, 1, 1, 1, 2; 3, 4, 4, 4, 3][A[k], ]))); A[n])} /* Michael Somos, May 16 2005 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|