A059954 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.)

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

Offset

1,1

Comments

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).

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 A333103 A139257

Adjacent sequences: A059951 A059952 A059953 * A059955 A059956 A059957

Keyword

nonn

Author

John W. Layman, Mar 13 2001

Status

approved