A321246 Non-isomorphic proper colorings of the 5 X 5 grid graph using at most n colors under rotational and reflectional symmetries.

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

Table of n, a(n) for n=1..17.

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

Cf. A002817, A321244, A321245.

Sequence in context: A272248 A195003 A071067 * A371645 A060069 A354177

Adjacent sequences: A321243 A321244 A321245 * A321247 A321248 A321249

Keyword

nonn

Author

Marko Riedel, Nov 01 2018

Status

approved