A321245 Non-isomorphic proper colorings of the 4 X 4 grid graph using at most n colors under rotational and reflectional symmetries.

0, 1, 1155, 759759, 103786510, 4767856260, 107118740001, 1465350136810, 13956101513964, 100946621623995, 588405869207695, 2882842751900001, 12245455022841690, 46164185630256694, 157281327978056205, 491245336843482180, 1422828159652548376, 3857444027819847045, 9864873410828916699, 23951146853875652515, 55509091777214287590

Offset: 1

Author

Marko Riedel, Nov 01 2018

Keywords

• nonn

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.

Crossrefs

Cf. A002817, A321244, A321246.

Formula

a(n) = (1/8)*n^16 - 3*n^15 + (69/2)*n^14 - (2015/8)*n^13 + (10437/8)*n^12 - (20307/4)*n^11 + 15333*n^10 - (292907/8)*n^9 + (557915/8)*n^8 - (848501/8)*n^7 + (1023195/8)*n^6 - (240539/2)*n^5 + (683997/8)*n^4 - (347485/8)*n^3 + (112831/8)*n^2 - (8807/4)*n.