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A052497
Nonsingular n X n matrices over GF(9).
7
1, 8, 5760, 339655680, 1624314979123200, 629282246371356907929600, 19747506525777609095698646040576000, 50195501537943419769100848121708339934527488000
OFFSET
0,2
LINKS
J. Overbey, W. Traves and J. Wojdylo, On the Keyspace of the Hill Cipher.
FORMULA
a(n) = (9^n - 1)*(9^n - 9)*...*(9^n - 9^(n-1)).
a(n) = A053764(n)*A027877(n). - Bruno Berselli, Jan 30 2013
MATHEMATICA
Table[Product[(9^n - 9^j), {j, 0, n-1}], {n, 0, 10}] (* G. C. Greubel, May 14 2019 *)
PROG
(Magma) [1] cat [&*[(9^n - 9^k): k in [0..n-1]]: n in [1..10]]; // Bruno Berselli, Jan 28 2013
(PARI) {a(n) = prod(j=0, n-1, 9^n - 9^j)}; \\ G. C. Greubel, May 14 2019
(Sage) [product(9^n - 9^j for j in (0..n-1)) for n in (0..10)] # G. C. Greubel, May 14 2019
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Mar 16 2000
STATUS
approved