

A059954


Number of 2 X 2 matrices with elements from {0,1,2,...,n} and with NimDeterminant 1. (The NimDeterminant of the 2 X 2 matrix [a,b; c,d] is defined to be a*d xor b*c, where * denotes NimMultiplication.)


0



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

1,1


COMMENTS

The six 2 X 2 matrices of 0's and 1's with NimDeterminant 1, the 60 with elements 0,1,2 and 3 and the 4080 with elements from {0,1,...,15} form groups under NimMatrixmultiplication (use the corresponding Nim operation instead of ordinary multiplication and addition/subtraction).


REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, ``Winning Ways'', p. 443 J. H. Conway, ``On Numbers and Games'', chapter 6


LINKS

Table of n, a(n) for n=1..43.


CROSSREFS

Sequence in context: A107301 A118432 A032404 * A252541 A139257 A056842
Adjacent sequences: A059951 A059952 A059953 * A059955 A059956 A059957


KEYWORD

nonn


AUTHOR

John W. Layman, Mar 13 2001


STATUS

approved



