A053765 a(n) = 4^(n^2 - n).

1, 1, 16, 4096, 16777216, 1099511627776, 1152921504606846976, 19342813113834066795298816, 5192296858534827628530496329220096, 22300745198530623141535718272648361505980416

Offset: 0

Author

Stephen G Penrice, Mar 29 2000

Keywords

• easy
• nonn

Comments

Number of nilpotent n X n matrices over GF(4).

(-1)^n * resultant of the Chebyshev polynomial of first kind of degree n and Chebyshev polynomial of first kind of degree 2n (cf. A039991). - Benoit Cloitre, Jan 26 2003

a(n) is the number of spanning subgraphs (or equivalently sets of edges) in the n X n grid graph. - Andrew Howroyd, Jan 29 2023

References

• N. J. Fine and I. N. Herstein, The probability that a matrix be nilpotent, Illinois J. Math., 2 (1958), 499-504.
• M. Gerstenhaber, On the number of nilpotent matrices with coefficients in a finite field. Illinois J. Math., Vol. 5 (1961), 330-333.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A053763, A053764.

Programs

PARI

a(n) = 4^(n^2 - n) \\ Andrew Howroyd, Jan 29 2023

Extensions

More terms from James Sellers, Apr 08 2000