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Search: id:A140822
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| A140822 |
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A generalized Pascal's triangle type of triangular sequence; t(n,m)=Binomial[n,GCD[n,m]]. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 5, 5, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 28, 8, 70, 8, 28, 8, 1, 1, 9, 9, 84, 9, 9, 84, 9, 9, 1, 1, 10, 45, 10, 45, 252, 45, 10, 45, 10, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 2, 4, 8, 16, 22, 64, 44, 160, 224, 474}
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FORMULA
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t(n,m)=Binomial[n,GCD[n,m]].
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 4, 6, 4, 1},
{1, 5, 5, 5, 5, 1},
{1, 6, 15, 20, 15, 6, 1},
{1, 7, 7, 7, 7, 7, 7, 1},
{1, 8, 28, 8, 70, 8, 28, 8, 1},
{1, 9, 9, 84, 9, 9, 84, 9, 9, 1},
{1, 10, 45, 10, 45, 252, 45, 10, 45, 10, 1}
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MATHEMATICA
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a = Table[Table[Binomial[n, GCD[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A123264 A034930 A095142 this_sequence A089239 A061676 A095145
Adjacent sequences: A140819 A140820 A140821 this_sequence A140823 A140824 A140825
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 16 2008
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