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Search: id:A059954
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| A059954 |
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Number of 2 X 2 matrices with elements from {0,1,2,...,n} and with Nim-Determinant 1. (The Nim-Determinant of the 2 X 2 matrix [a,b; c,d] is defined to be a*d xor b*c, where * denotes Nim-Multiplication.) |
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+0
1
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| 6, 14, 60, 72, 106, 150, 240, 360, 598, 902, 1308, 1812, 2378, 3146, 4080, 4140, 4270, 4346, 4500, 4592, 4754, 4910, 5144, 5308, 5558, 5802, 6140, 6440, 6826, 7206, 7680, 8168, 8702, 9322, 9996, 10676, 11418, 12278, 13208, 14152, 15158, 16306, 17540
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OFFSET
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1,1
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COMMENT
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The six 2 X 2 matrices of 0's and 1's with Nim-Determinant 1, the 60 with elements 0,1,2 and 3 and the 4080 with elements from {0,1,...,15} form groups under Nim-Matrix-multiplication (use the corresponding Nim operation instead of ordinary multiplication and addition/subtraction).
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, ``Winning Ways'', p. 443 J. H. Conway, ``On Numbers and Games'', chapter 6
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CROSSREFS
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Adjacent sequences: A059951 A059952 A059953 this_sequence A059955 A059956 A059957
Sequence in context: A107301 A118432 A032404 this_sequence A139257 A056842 A130263
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Mar 13 2001
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