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.

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

Adjacent sequences: A059829 A059830 A059831 * A059833 A059834 A059835

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