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
Examples
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] ...
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
Crossrefs
Programs
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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
Formula
a(n) = A059825(n) + 1. - Sean A. Irvine, Oct 11 2022
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), Feb 26 2001
Entry revised by N. J. A. Sloane, Jun 21 2018
Comments