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Python

from itertools import zip_longest
from sympy.ntheory.factor_ import digits
from networkx import empty_graph, find_cliques
def A290607(n):
    k = 1<<(n<<1)
    G = empty_graph(range(k))
    G.add_edges_from((a,b) for a in range(k) for b in range(a) if (s:=tuple(c-d&3 for c, d in zip_longest(digits(a,4)[-1:0:-1],digits(b,4)[-1:0:-1],fillvalue=0))).count(2)==0 or s.count(0)>len(s)-2)
    return sum(1 for c in find_cliques(G)) # Chai Wah Wu, Jan 11 2024