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A059832
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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.
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7
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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
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OFFSET
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0,2
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COMMENTS
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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) ...
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REFERENCES
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C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 273.
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LINKS
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C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
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FORMULA
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EXAMPLE
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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]
...
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MAPLE
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# 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]);
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CROSSREFS
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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.
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 26 2001
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STATUS
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approved
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