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Search: id:A118233
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| A118233 |
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Triangle, read by rows, equal to the matrix square of triangle A054431. |
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+0
3
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| 1, 2, 1, 2, 0, 1, 4, 2, 2, 1, 2, 0, 0, 0, 1, 6, 3, 3, 2, 2, 1, 4, 0, 2, 0, 2, 0, 1, 6, 3, 2, 2, 3, 0, 2, 1, 4, 0, 3, 0, 1, 0, 2, 0, 1, 10, 5, 6, 4, 5, 2, 4, 2, 2, 1, 4, 0, 1, 0, 3, 0, 2, 0, 0, 0, 1, 12, 6, 7, 5, 7, 3, 6, 3, 3, 2, 2, 1, 6, 0, 3, 0, 3, 0, 2, 0, 2, 0, 2, 0, 1, 8, 4, 3, 3, 4, 0, 4, 2, 1, 0, 3, 0, 2
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Describes the sequence transformation of triangle A054431 iterated twice. Also, equals the matrix inverse of triangle A118231.
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FORMULA
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Column 1: T(n,1) = phi(n). Column 2: T(2*n-1,2) = 0; T(2*n,2) = phi(2*n+1)/2. Column 3: T(3*n-1) = phi(3*n)/2 - 1. Column 4: T(2*n-1,4) = 0; T(2*n,4) = phi(2*n+1)/2 - 1.
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EXAMPLE
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Triangle begins:
1;
2, 1;
2, 0, 1;
4, 2, 2, 1;
2, 0, 0, 0, 1;
6, 3, 3, 2, 2, 1;
4, 0, 2, 0, 2, 0, 1;
6, 3, 2, 2, 3, 0, 2, 1;
4, 0, 3, 0, 1, 0, 2, 0, 1;
10, 5, 6, 4, 5, 2, 4, 2, 2, 1;
4, 0, 1, 0, 3, 0, 2, 0, 0, 0, 1;
12, 6, 7, 5, 7, 3, 6, 3, 3, 2, 2, 1;
6, 0, 3, 0, 3, 0, 2, 0, 2, 0, 2, 0, 1;
8, 4, 3, 3, 4, 0, 4, 2, 1, 0, 3, 0, 2, 1; ...
where column 1 forms Euler totient function phi(n).
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PROGRAM
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(PARI) {T(n, k)=local(M=matrix(n, n, r, c, if(r>=c, if(gcd(r-c+1, c)==1, 1, 0)))^2); M[n, k]}
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CROSSREFS
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Cf. A054431, A118231 (matrix inverse).
Sequence in context: A129559 A129680 A118231 this_sequence A053838 A117167 A117169
Adjacent sequences: A118230 A118231 A118232 this_sequence A118234 A118235 A118236
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KEYWORD
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nonn,tabl
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2006
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