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%I #26 Sep 13 2019 21:58:43
%S 1,27,35,84,168,1,168,195,819,2457,1,650,714,4368,17472,1,1890,2015,
%T 16275,81375,1,9632,9975,120099,840693,1,18468,18980,266304,2130432,1,
%U 32850,33579,538083,4842747,1,87912,89243,1786323,19649553,1,200018,202215,4855539,63122007
%N Multiplicities of 4-class association schemes.
%C The rows are of length 5, always beginning with a 1. Each row corresponds to a term of A246655. This arises from constructing the character table for the association scheme generated by the action of the symplectic group Sp(6,q) acting on the Cartesian product of totally isotropic subspaces of dimension 2.
%F row(n) = (1, (1/2)*(q+1)*(q^3+1)*q, (1/2)*q*(q^2+1)*(q^2+q+1), q^2*(q^4+q^2+1), q^3*(q^4+q^2+1)), where q = A246655(n).
%e For n=1, we have q = A246655(1) = 2. So, row(1) = (1, 27, 35, 84, 168).
%o (PARI) row(q) = [1, (1/2)*(q+1)*(q^3+1)*q, (1/2)*q*(q^2+1)*(q^2+q+1), q^2*(q^4+q^2+1), q^3*(q^4+q^2+1)];
%o lista(nn) = {for (k=1, nn, if (isprimepower(k), my(row = row(k)); for (i=1, 5, print1(row[i], ", "));););} \\ _Michel Marcus_, Sep 13 2019
%Y Cf. A246655 (prime powers, p^k for k>=1).
%K nonn,tabf
%O 1,2
%A _Robert Lazar_, Sep 13 2019
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