A053766 - OEIS

A053766

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

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

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OFFSET

0,3

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.

LINKS

FORMULA

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

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 *)

CROSSREFS

KEYWORD

easy,nonn

AUTHOR

EXTENSIONS

More terms from James A. Sellers, Apr 08 2000

STATUS

approved