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1, 3, 1, 3, 0, 1, 6, 3, 0, 1, 3, 0, 0, 0, 1, 9, 3, 3, 0, 0, 1, 3, 0, 0, 0, 0, 0, 1, 10, 6, 0, 3, 0, 0, 0, 1, 6, 0, 3, 0, 0, 0, 0, 0, 1, 9, 3, 0, 0, 0, 3, 0, 0, 0, 0, 1
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refs;
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history;
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OFFSET
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1,2
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COMMENTS
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Nonzero terms in every column = A007425: (1, 3, 3, 6, 3, 9, 3, ...).
Row sums = A007426: (1, 4, 4, 20, 4, 16, ...).
A127172 * mu(n) = d(n); or A127172 * A008683 = A000005.
A127172 * d(n) = tau_5(n); or A127172 * A000005 = A061200.
A127172 * phi(n) = A007429: (1, 4, 5, 11, 7, 20, ...); or: A127172 * A000010 = A007429.
Note that A051731 * d(n) = row sums of A127172; or A051731 * A000005 = A007425.
Also, A126988 * mu(n) = phi(n); or A126988 * A008683 = A000010.
A126988 * phi(n) = A018804: (1, 3, 5, 8, 9, 15, ...); = A127170 * mu(n).
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LINKS
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Table of n, a(n) for n=1..56.
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FORMULA
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Cube of A051731 A007425: (1, 3, 3, 6, 3, 9, 3, ...) in every column k, interspersed with (k-1) zeros.
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EXAMPLE
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First few rows of the triangle:
1;
3, 1;
3, 0, 1;
6, 3, 0, 1;
3, 0, 0, 0, 1;
9, 3, 3, 0, 0, 1;
3, 0, 0, 0, 0, 0, 1;
10, 6, 0, 3, 0, 0, 0, 1;
6, 0, 3, 0, 0, 0, 0, 0, 1;
9, 3, 0, 0, 3, 0, 0, 0, 0, 1;
...
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CROSSREFS
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Cf. A000005, A007425, A127170, A051731, A007429, A000010, A126988, A018804.
Sequence in context: A136157 A266260 A143353 * A011087 A180021 A091422
Adjacent sequences: A127169 A127170 A127171 * A127173 A127174 A127175
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Gary W. Adamson, Jan 06 2007
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STATUS
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approved
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