cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A071309 #10 Nov 07 2022 02:22:25
%S A071309 1,12,1320,1742400,25721308800,4145554781913600,
%T A071309 7338585441586912128000,142998501741091915820267520000,
%U A071309 30655092458961006120118267244605440000,72283553302207308288060341547889057722286080000
%N A071309 a(n) = (1/2) * (number of n X n 0..10 matrices with MM' mod 11 = I).
%C A071309 Also, number of n X n orthogonal matrices over GF(11) with determinant 1. - _Max Alekseyev_, Nov 06 2022
%H A071309 Jessie MacWilliams, <a href="https://doi.org/10.2307/2317262">Orthogonal Matrices Over Finite Fields</a>, The American Mathematical Monthly 76:2 (1969), 152-164.
%F A071309 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
%o A071309 (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
%Y A071309 Cf. A071302, A071303, A071304, A071305, A071306, A071307, A071308, A071310.
%K A071309 nonn
%O A071309 1,2
%A A071309 _R. H. Hardin_, Jun 11 2002
%E A071309 Terms a(6) onward from _Max Alekseyev_, Nov 06 2022