A071309 a(n) = (1/2) * (number of n X n 0..10 matrices with MM' mod 11 = I).

1, 12, 1320, 1742400, 25721308800, 4145554781913600, 7338585441586912128000, 142998501741091915820267520000, 30655092458961006120118267244605440000, 72283553302207308288060341547889057722286080000

Offset: 1

Author

R. H. Hardin, Jun 11 2002

Keywords

• nonn

Comments

Also, number of n X n orthogonal matrices over GF(11) with determinant 1. - Max Alekseyev, Nov 06 2022

Links

• Jessie MacWilliams, Orthogonal Matrices Over Finite Fields, The American Mathematical Monthly 76:2 (1969), 152-164.

Crossrefs

Cf. A071302, A071303, A071304, A071305, A071306, A071307, A071308, A071310.

Programs

PARI

{ a071309(n) = my(t=n\2); prod(i=0, t-1, 11^(2*t)-11^(2*i)) * if(n%2, 11^t, 1/(11^t+(-1)^t)); } \\ Max Alekseyev, Nov 06 2022

Formula

a(2k+1) = 11^k * Product_{i=0..k-1} (11^(2k) - 11^(2i)); a(2k) = (11^k + (-1)^(k+1)) * Product_{i=1..k-1} (11^(2k) - 11^(2i)) (see MacWilliams, 1969). - Max Alekseyev, Nov 06 2022

Extensions

Terms a(6) onward from Max Alekseyev, Nov 06 2022