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A059832
A ternary tribonacci triangle: form the triangle as follows: start with 3 single values: 1, 2, 3. Each succeeding row is a concatenation of the previous 3 rows.
7
1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3
OFFSET
0,2
COMMENTS
Alternatively, define a morphism f: 1 -> 2, 2 -> 3, 3 -> 1,2,3; let S(0)=1, S(k) = f(S(k-1)) for k>0; then sequence is the concatenation S(0) S(1) S(2) S(3) ...
REFERENCES
C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 273.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..30121 (Roes 0 through 17, flattened.)
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
FORMULA
a(n) = A059825(n) + 1. - Sean A. Irvine, Oct 11 2022
EXAMPLE
Rows 0, 1, 2, ..., 8, ... of the triangle are:
0, [1]
1, [2]
2, [3]
3, [1, 2, 3]
4, [2, 3, 1, 2, 3]
5, [3, 1, 2, 3, 2, 3, 1, 2, 3]
6, [1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3]
7, [2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3]
8, [3, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 2, 3, 1, 2, 3]
...
MAPLE
# To get successive rows of A059832
S:=Array(0..100);
S[0]:=[1];
S[1]:=[2];
S[2]:=[3];
for n from 3 to 12 do
S[n]:=[op(S[n-3]), op(S[n-2]), op(S[n-1])];
lprint(S[n]);
od: # N. J. A. Sloane, Jul 04 2018
CROSSREFS
Cf. A059835. Row sums A001590, row lengths A000213.
Rows 0,3,6,9,12,... converge to A305389, rows 1,4,7,10,... converge to A305390, and rows 2,5,8,11,... converge to A305391.
Sequence in context: A194871 A194899 A228094 * A105316 A105933 A105315
KEYWORD
easy,nonn,tabf
AUTHOR
Jason Earls, Feb 25 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Feb 26 2001
Entry revised by N. J. A. Sloane, Jun 21 2018
STATUS
approved