A326893 Multiplicities of 4-class association schemes.

1, 27, 35, 84, 168, 1, 168, 195, 819, 2457, 1, 650, 714, 4368, 17472, 1, 1890, 2015, 16275, 81375, 1, 9632, 9975, 120099, 840693, 1, 18468, 18980, 266304, 2130432, 1, 32850, 33579, 538083, 4842747, 1, 87912, 89243, 1786323, 19649553, 1, 200018, 202215, 4855539, 63122007

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..45.

Formula

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).

Example

For n=1, we have q = A246655(1) = 2. So, row(1) =  (1, 27, 35, 84, 168).

Prog

(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)];
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

Crossrefs

Cf. A246655 (prime powers, p^k for k>=1).

Sequence in context: A134101 A226191 A098883 * A160119 A160379 A351473

Adjacent sequences: A326890 A326891 A326892 * A326894 A326895 A326896

Keyword

nonn,tabf

Author

Robert Lazar, Sep 13 2019

Status

approved