A105202 Irregular triangle read by rows: row n gives the word f(f(f(...(1)))) [with n applications of f], where f is the morphism 1->{1,2,1}, 2->{2,3,2}, 3->{3,1,3}.

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

Offset

0,3

Comments

Row n contains 3^n symbols.

Links

Antti Karttunen, Table of n, a(n) for n = 0..9840

F. M. Dekking, Recurrent sets, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104; page 96, section 4.10.

Formula

Let r = A062153(1+(2*n)) [index of the row], let c = n - A003462(r) [index of the column], then a(n) = 1 + (a(A003462(r-1)+floor(c/3)) mod 3) if n ≡ 2 mod 3, otherwise a(n) = a(A003462(r-1)+floor(c/3)). - Antti Karttunen, Aug 12 2017

Example

From Antti Karttunen, Aug 12 2017: (Start)
The rows 0 .. 3 of this irregular triangle:
  1
  1;2;1
  1 2 1;2 3 2;1 2 1;
  1 2 1 2 3 2 1 2 1;2 3 2 3 1 3 2 3 2;1 2 1 2 3 2 1 2 1
(End)

Mathematica

f[n_] := Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {2, 3, 2}, 3 -> {3, 1, 3}}] &, {1}, n]; Flatten[ Table[ f[n], {n, 0, 4}]] (* Robert G. Wilson v, Apr 12 2005 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A105202 n) (if (zero? n) 1 (let* ((r (A062153 (+ 1 (* 2 n)))) (c (- n (A003462 r))) (p (A105202 (+ (A003462 (- r 1)) (/ (- c (modulo c 3)) 3))))) (if (= 2 (modulo n 3)) (+ 1 (modulo p 3)) p))))
;; Antti Karttunen, Aug 12 2017

Crossrefs

Cf. A003462, A062153, A073058, A105141.

Each row is a prefix of A105203.

Sequence in context: A137900 A025837 A111317 * A240236 A356606 A099386

Adjacent sequences: A105199 A105200 A105201 * A105203 A105204 A105205

Keyword

nonn,tabf

Author

Roger L. Bagula, Apr 09 2005

Extensions

More terms from Robert G. Wilson v, Apr 12 2005

Status

approved