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Search: id:A069480
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| A069480 |
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Determinant of rank n matrix of 1..n^2 filled successively along antidiagonals. |
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+0
4
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| 1, -2, -5, 6, 13, -12, -25, 20, 41, -30, -61, 42, 85, -56, -113, 72, 145, -90, -181, 110, 221, -132, -265, 156, 313, -182, -365, 210, 421, -240, -481, 272, 545, -306, -613, 342, 685, -380, -761, 420, 841, -462, -925, 506, 1013, -552, -1105, 600, 1201, -650, -1301, 702, 1405, -756, -1513
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The sorted absolute values of this sequence begin: 1, 2, 5, 6, 12, 13, 20, 25, 30, 41, 42, 56, 61, 72, 85, 90, 110, 113, 132, 145, 156, 181, 182,
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REFERENCES
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On comp.soft-sys.math.mathematica (Mar 20 2002) Diamond Mark. R. asked for a nice way to generate matrices 'along the diagonals' of the form (see example). The coding is via Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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FORMULA
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a(n) = n*(n+2)/4, n = 0 mod 4; (n^2+1)/2, n = 1 mod 4; -n*(n+2)/4, n = 2 mod 4; -(n^2+1)/2, n = 3 mod 4; g.f. is x (x^4 - 2 x^2 - 2 x + 1) / (x^2 + 1)^3
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EXAMPLE
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a(4) = 6 = 4*6/4 = |1 3 6 10 | 2 5 9 13 | 4 8 12 15 | 7 11 14 16|.
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MATHEMATICA
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f[n_] := Table[(i + j - 1)((i + j - 1) - 1)/2 + 1 + (j - 1) - Mod[i + j - 1, n, 1]^2 Quotient[i + j - 1, n, 1], {i, n}, {j, n}]; Table[ Det[ f[n]], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A064765 A082552 A057683 this_sequence A100613 A070911 A113240
Adjacent sequences: A069477 A069478 A069479 this_sequence A069481 A069482 A069483
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KEYWORD
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easy,sign
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com) and Marc LeBrun (mlb(AT)well.com), Mar 26 2002
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