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Search: id:A113310
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| A113310 |
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Riordan array ((1+x)/(1-x),x/(1+x)). |
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+0
4
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| 1, 2, 1, 2, 1, 1, 2, 1, 0, 1, 2, 1, 1, -1, 1, 2, 1, 0, 2, -2, 1, 2, 1, 1, -2, 4, -3, 1, 2, 1, 0, 3, -6, 7, -4, 1, 2, 1, 1, -3, 9, -13, 11, -5, 1, 2, 1, 0, 4, -12, 22, -24, 16, -6, 1, 2, 1, 1, -4, 16, -34, 46, -40, 22, -7, 1, 2, 1, 0, 5, -20, 50, -80, 86, -62, 29, -8, 1, 2, 1, 1, -5, 25, -70, 130, -166, 148, -91, 37, -9, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums are A113311. Diagonal sums are A113312. Inverse is A113313. The family of Riordan arrays ((1+x)/(1-(q-1)x),x/(1+x)) allow one to calculate the weight distribution of MDS codes.
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REFERENCES
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F.J. MacWilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 2003, p. 321.
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FORMULA
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T(n, k)=sum{j=0..n-k, (-1)^j*C(j+k-2, i)}; T(n, k)=sum{j=0..n-k, (-1)^(n-k-j)C(n-j-2, n-j-k); T(n, k)=sum{j=k..n, (-1)^(n-j)*C(n, j)(2^(j-k+1)-1).
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EXAMPLE
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Triangle begins
1;
2,1;
2,1,1;
2,1,0,1;
2,1,1,-1,1;
2,1,0,2,-2,1;
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CROSSREFS
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Sequence in context: A003639 A061916 A076348 this_sequence A081653 A096860 A128185
Adjacent sequences: A113307 A113308 A113309 this_sequence A113311 A113312 A113313
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 25 2005
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