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A326893 Multiplicities of 4-class association schemes. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabf
AUTHOR
Robert Lazar, Sep 13 2019
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)