The alphabet may be any set of size 4 (GF(4), Z/4Z, etc.) so there is no requirement of linearity.
a(6) is known to be in the range [164-179], and a(7) in the range [512-614].
Table of n, a(n) for n=1..5.
N. J. A. Sloane, Challenge Problems: Independent Sets in Graphs
R. Barden, N. Bushaw, C. Callison, A. Fernandez, B. Harris, I. Holden, C. E. Larson, D. Muncy, C. O'Shea, J. Shive, J. Raines, P. Rana, N. van Cleemput, B. Ward, and N. Wilcox-Cook, The Graph Brain Project & Big Mathematics, research paper, 2017.
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Oleksandra Yezerska and Sergiy Butenko, The Maximum Clique and Vertex Coloring, Handbook of Heuristics. Springer, Cham, 2018, 1-31.
Bogdán Zaválnij, The k-Clique Problem--Usage, Modeling Expressivity, Serial and Massively Parallel Algorithms, Ph. D. Dissertation, University of Szeged (Hungary, 2020).