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Search: id:A127013
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| 1, 1, 2, 1, 0, 3, 1, 0, 2, 4, 1, 0, 0, 0, 5, 1, 0, 0, 2, 3, 6, 1, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 2, 0, 4, 8, 1, 0, 0, 0, 0, 0, 3, 0, 9, 1, 0, 0, 0, 0, 2, 0, 0, 5, 1, 0
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Let j = reversed indices of row terms. Then for any row, j*T(n,k) = n, for non-zero T(n,k). For example, in row 10, we match the terms with their j indices: (1, 0, 0, 0, 0, 2, 0, 0, 5, 10), (dot product) (10, 9, 8, 7, 6, 5, 4, 3, 2, 1); getting 10, 0, 0, 0, 0, 10, 0, 0, 10, 10). The factors of n are found in each row in order, as non-zero terms; e.g. 10 has the factors 1, 2, 5, 10, sum 18. Row sums = sigma(n), A000203.
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REFERENCES
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David Wells, "Prime Numbers, The Most Mysterious Figures in Math", John Wiley & Sons, 2005, Appendix.
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FORMULA
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Reversed rows of A126988
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EXAMPLE
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Row 10 = (1, 0, 0, 0, 0, 2, 0, 0, 5, 10), reversal of 10-th row of A126988.
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CROSSREFS
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Cf. A126988, A000203.
Sequence in context: A063173 A120111 A130055 this_sequence A117362 A113214 A029323
Adjacent sequences: A127010 A127011 A127012 this_sequence A127014 A127015 A127016
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 02 2007
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