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%I #20 Feb 12 2021 12:12:59
%S 0,2,76332,2557101612,6352711134515,2747239197568620,
%T 378972203462839707,23698347614119889312,832593421909253876202,
%U 18885862442806789810230,304064344379602597321190,3716359333313224494744012,36226784801918510547852117,292338319876651811428566992,2009992643746035728869251645,12045344786281525649136156960,64072515057361294676198896292
%N Non-isomorphic proper colorings of the 5 X 5 grid graph using at most n colors under rotational and reflectional symmetries.
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973.
%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2584928/">Tree graphs colorings</a>, Math StackExchange, December 2017.
%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2977453/">3-colourings of a 3×3 table with one of 3 colors up to symmetries</a>, Math StackExchange, October 2018.
%F a(n) = (1/8)*n^25 - 5*n^24 + (195/2)*n^23-1233*n^22 + (45399/4)*n^21 - 80919*n^20 + (928545/2)*n^19 - (17590911/8)*n^18 + (69997383/8)*n^17 - (118477969/4)*n^16 + (172111059/2)*n^15 - (1726958987/8)*n^14 + (3754019329/8)*n^13 - (1770719251/2)*n^12 + (5797425049/4)*n^11 - 2053661272*n^10 + (20055169857/8)*n^9 - (20932696169/8)*n^8 + (9236896437/4)*n^7 - (6780818949/4)*n^6 + (8083053959/8)*n^5 - (3768579695/8)*n^4 + (1292510453/8)*n^3 - (145271789/4)*n^2 + 4017958*n.
%Y Cf. A002817, A321244, A321245.
%K nonn
%O 1,2
%A _Marko Riedel_, Nov 01 2018
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