17 = A347301(n) <= a(11) <= A006855(11) = 18, but from [C. R. J. Clapham, A. Flockhart, J. Sheehan, Graphs without four-cycles, J. Graph Theory 13 (1) (1989) 29-47], all graphs with 11 nodes without 4-cycles and the maximum amount of edges (18 edges) are either one of the graphs in Figure 6 of the paper (the "new" graphs), or one of the graphs from Figure 5 with one more node ("old" graphs).
The new graphs are impossible by corollary 4.1 in https://oeis.org/A352178/a352178.pdf , and the old graphs are impossible, as they contain the two graphs proven to be impossible in this same paper.

So a(17) is not 18, and must be 17.