[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A053293 revision #24

A053293
Number of nonsingular n X n matrices over GF(7).
14
1, 6, 2016, 33784128, 27811094169600, 1122211189922928537600, 2218959336124989671614429593600, 214992513152176999576908105619651923148800, 1020690003311610463765638355505358381593396977336320000, 237443634207909205360438080389756681126654524500073656592021585920000
OFFSET
0,2
LINKS
J. Overbey, W. Traves and J. Wojdylo, On the Keyspace of the Hill Cipher.
FORMULA
a(n) = (7^n - 1)*(7^n - 7)*...*(7^n - 7^(n-1)).
a(n) = A109493(n)*A027875(n). - Bruno Berselli, Jan 30 2013
MATHEMATICA
Table[Product[7^n - 7^k, {k, 0, n-1}], {n, 0, 10}] (* Vincenzo Librandi, Jan 28 2013 *)
PROG
(MAGMA) [1] cat [&*[(7^n - 7^k): k in [0..n-1]]: n in [1..7]]; // Bruno Berselli, Jan 28 2013
(PARI) for(n=0, 10, print1(prod(k=0, n-1, 7^n - 7^k), ", ")) \\ G. C. Greubel, May 31 2018
CROSSREFS
Column k=7 of A316622.
Sequence in context: A341872 A024086 A094036 * A209737 A209458 A209520
KEYWORD
nonn,easy
AUTHOR
Stephen G. Penrice (spenrice(AT)ets.org), Mar 04 2000
EXTENSIONS
More terms from Vladeta Jovovic, Mar 16 2000
STATUS
proposed