0,3

Number of nilpotent n X n matrices X over GF(3), that is, the number of n X n matrices X over GF(3) satisfying X^k = 0 for some k >= 1.

More generally, Fine and Herstein prove that the probability that an n X n matrix over GF(p^m) is nilpotent is 1/p^(mn) and the probability that an n X n matrix over Z/mZ is nilpotent is 1/k^n, where k is the product of the distinct prime factors of m.

Is this the same sequence (apart from the initial term) as A053854? - Philippe DELEHAM, Dec 09 2007

[1,9,729,531441,3486784401,...] is the Hankel transform of A005159. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 10 2007

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.

Sequence given by the Hankel transform (see A001906 for definition) of A082181 = {1, 1, 10, 109, 1270, 15562, 198100, ...}; example : det([1, 1, 10, 109; 1, 10, 109, 1270; 10, 109, 1270, 15562; 109, 1270, 15562, 198100]) = 9^6 = 531441 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 20 2005

with(finance):seq(mul(futurevalue( 1, 2, n), k=0..n), n=-1..10); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 01 2008

Cf. A053763.

Sequence in context: A069034 A053847 A053854 this_sequence A122251 A015481 A145183

Adjacent sequences: A053761 A053762 A053763 this_sequence A053765 A053766 A053767

easy,nonn

Stephen G. Penrice (spenrice(AT)ets.org), Mar 29 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 08 2000