A107469 4-symbol substitution made from Cantor matrix by one level matrix self-similarity.

1, 1, 2, 3, 4, 3, 2, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 2, 2, 4, 4, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 4, 4, 3, 3, 3, 2, 2, 2, 4, 4, 4, 2, 2, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1

Offset

0,3

Comments

Matrix: M={{4, 2,2 1}, {0, 6, 0, 3}, {0, 0, 6, 3}, {0, 0, 0, 9}} Characteristic Polynomial: -x^4+25*x^3-228*x^2+900x-1296

Links

Table of n, a(n) for n=0..80.

F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 85, section 4.15, see Cantor set.

Formula

1->{1, 1, 2, 3, 4, 3, 2, 1, 1}, 2->{2, 2, 2, 4, 4, 4, 2, 2, 2}, 3->{3, 3, 3, 4, 4, 4, 3, 3, 3}, 4->{4, 4, 4, 4, 4, 4, 4, 4, 4}

Mathematica

s[1] = {1, 1, 2, 3, 4, 3, 2, 1, 1}; s[2] = {2, 2, 2, 4, 4, 4, 2, 2, 2}; s[3] = {3, 3, 3, 4, 4, 4, 3, 3, 3}; s[4] = {4, 4, 4, 4, 4, 4, 4, 4, 4}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[3]

Crossrefs

Sequence in context: A179764 A266313 A017869 * A167600 A008287 A017859

Adjacent sequences: A107466 A107467 A107468 * A107470 A107471 A107472

Keyword

nonn,uned

Author

Roger L. Bagula, May 27 2005

Status

approved