A052497 Nonsingular n X n matrices over GF(9).

1, 8, 5760, 339655680, 1624314979123200, 629282246371356907929600, 19747506525777609095698646040576000, 50195501537943419769100848121708339934527488000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..30

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

Crossrefs

Cf. A027877, A053764.

Cf. A002884, A003792, A053290, A053291, A053292, A053293, A052496, A052498.

Sequence in context: A318897 A178329 A062030 * A304426 A316281 A305960

Adjacent sequences: A052494 A052495 A052496 * A052498 A052499 A052500

Keyword

nonn,easy

Author

Vladeta Jovovic, Mar 16 2000

Status

approved