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Search: id:A078475
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| A078475 |
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Determinant of rank n matrix of 1..n^2 filled successively back and forth along antidiagonals. |
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+0
4
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| 1, -2, 15, -594, -5187, 23244, 122475, -279292, -1157143, 1850930, 6642839, -8529278, -27810555, 30741424, 93575187, -92784984, -268191855, 244875462, 679807583, -581798410
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OFFSET
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1,2
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COMMENT
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The matrix is formed by writing numbers 1 .. n^2 in zig-zag pattern as shown in examples below. Every other antidiagonal reads backwards from A069480.
Whereas each antidiagonal of A069480 begins with one more than a triangular number and ends with the next triangular number, here every other antidiagonal begins with one more than a triangular number and the next antidiagonal begins with a triangular number.
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EXAMPLE
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n=2, det=-2: {1 2 / 3 4 }
n=3, det=15: {1 2 6 / 3 5 7 / 4 8 9 }
n=4, det=-594: { 1 2 6 7 / 3 5 8 13 / 4 9 12 14 / 10 11 15 16 }
n=5, det=-5187: { 1 2 6 7 15 / 3 5 8 14 16 / 4 9 13 17 22 / 10 12 18 21 23 / 11 19 20 24 25 }
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CROSSREFS
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Cf. A079340, A069480, A023999.
Sequence in context: A013098 A158109 A136463 this_sequence A015185 A071627 A013064
Adjacent sequences: A078472 A078473 A078474 this_sequence A078476 A078477 A078478
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KEYWORD
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sign
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AUTHOR
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Kit Vongmahadlek (kit119(AT)yahoo.com), Jan 03 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), May 08 2003
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