This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337518 #19 Jul 04 2024 20:05:00 %S A337518 1,1,2,1,2,1,0,0,1,0,2,2,0,0,1,2,0,1,0,2,1,2,0,0,2,0,0,1,1,1,0,0,2,0, %T A337518 1,0,2,1,0,0,2,2,0,2,0,0,2,1,2,1,0,1,0,1,1,1,0,1,2,2,1,0,1,2,0,1,2,1, %U A337518 1,1,1,0,0,2,1,1,2,0,2,0,0,0,2,1,2,2,1 %N A337518 Number of non-isomorphic graphs on n unlabeled nodes modulo 3. %C A337518 For the mod-2 case, the sequence is eventually constant, because there are an even number of graphs on n vertices for n>4. (In fact, the number of factors of 2 in A000088(n) is asymptotically n/2; see Cater and Robinson in the Links section.) %H A337518 Chai Wah Wu, <a href="/A337518/b337518.txt">Table of n, a(n) for n = 0..98</a> %H A337518 Steven C. Cater and Robert W. Robinson, <a href="http://cobweb.cs.uga.edu/~rwr/publications/techtournament.pdf">Exponents of 2 in the numbers of unlabeled graphs and tournaments</a>, Congressus Numerantium, 82 (1991), pp. 139-155. %F A337518 a(n) = A000088(n) mod 3. %e A337518 For n = 4, there are 11 graphs on 4 nodes up to isomorphism, so a(4) = 2 = 11 mod 3. %o A337518 (Python) %o A337518 from itertools import combinations %o A337518 from math import prod, factorial, gcd %o A337518 from fractions import Fraction %o A337518 from sympy.utilities.iterables import partitions %o A337518 def A337518(n): return int(sum(Fraction(1<<sum(p[r]*p[s]*gcd(r,s) for r,s in combinations(p.keys(),2))+sum((q>>1)*r+(q*r*(r-1)>>1) for q, r in p.items()),prod(q**r*factorial(r) for q, r in p.items()))%3 for p in partitions(n))) % 3 # _Chai Wah Wu_, Jul 02 2024 %Y A337518 Cf. A000088, A007149. %K A337518 nonn %O A337518 0,3 %A A337518 _Drake Thomas_, Nov 21 2020