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A321246
Non-isomorphic proper colorings of the 5 X 5 grid graph using at most n colors under rotational and reflectional symmetries.
2
0, 2, 76332, 2557101612, 6352711134515, 2747239197568620, 378972203462839707, 23698347614119889312, 832593421909253876202, 18885862442806789810230, 304064344379602597321190, 3716359333313224494744012, 36226784801918510547852117, 292338319876651811428566992, 2009992643746035728869251645, 12045344786281525649136156960, 64072515057361294676198896292
OFFSET
1,2
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973.
LINKS
Marko Riedel et al., Tree graphs colorings, Math StackExchange, December 2017.
Marko Riedel et al., 3-colourings of a 3×3 table with one of 3 colors up to symmetries, Math StackExchange, October 2018.
FORMULA
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Riedel, Nov 01 2018
STATUS
approved