A053766 a(n) = 5^(n^2 - n).

1, 1, 25, 15625, 244140625, 95367431640625, 931322574615478515625, 227373675443232059478759765625, 1387778780781445675529539585113525390625

Offset: 0

Author

Stephen G Penrice, Mar 29 2000

Keywords

• easy
• nonn

Comments

Number of nilpotent n X n matrices over GF(5).

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.

Crossrefs

Cf. A053763, A053764, A053765.

Programs

Maple

A053766:=n->5^(n^2 - n); seq(A053766(n), n=0..10); # Wesley Ivan Hurt, Jan 28 2014

Mathematica

Table[5^(n^2 - n), {n, 0, 10}] (* Wesley Ivan Hurt, Jan 28 2014 *)

Formula

a(n) = A000351(n^2 - n). - Wesley Ivan Hurt, Jan 28 2014

Extensions

More terms from James Sellers, Apr 08 2000