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Search: id:A119947
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| A119947 |
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Triangle of numerators of the square of a certain lower triangular matrix. |
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+0
4
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| 1, 3, 1, 11, 5, 1, 25, 13, 7, 1, 137, 77, 47, 9, 1, 49, 29, 19, 37, 11, 1, 363, 223, 153, 319, 107, 13, 1, 761, 481, 341, 743, 533, 73, 15, 1, 7129, 4609, 3349, 2509, 1879, 275, 191, 17, 1, 7381, 4861, 3601, 2761, 2131
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The triangle of the corresponding denominators is A119948. The rationals appear in lowest terms.
The triangle with row number i multiplied with the least commom multiple (LCM) of its denominators yields A027446.
First column is A001008 [From Tilman Neumann (Tilman.Neumann(AT)web.de), Oct 01 2008]
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LINKS
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W. Lang: First ten rows and rationals.
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FORMULA
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a(i,j)= numerator(r(i,j)) with r(i,j):=(A^2)[i,j], where the matrix A has elements a[i,j] = 1/i if j<=i, 0 if j>i, (lower triangular).
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EXAMPLE
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The rationals are [1];[ 3/4,1/4 ];[ 11/18,5/18,1/9
];[25/48,13/48,7/48,1/16];... See the W. Lang link for more.
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CROSSREFS
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a(i, j)=1/A002024(i, j), i>=1, j<=i.
Row sums give A119949. Row sums of the triangle of rationals give always 1.
For the cube of this matrix see the rational triangle A119935/A119932 and A027447.
Sequence in context: A166752 A120291 A099001 this_sequence A165674 A027446 A027516
Adjacent sequences: A119944 A119945 A119946 this_sequence A119948 A119949 A119950
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KEYWORD
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nonn,easy,frac,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
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