A321244 -id:A321244 - cp's OEIS frontend

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

Marko Riedel, Nov 01 2018

nonn

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973.

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.

Cf. A002817, A321244, A321246.

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.

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

Original entry on oeis.org

0, 2, 76332, 2557101612, 6352711134515, 2747239197568620, 378972203462839707, 23698347614119889312, 832593421909253876202, 18885862442806789810230, 304064344379602597321190, 3716359333313224494744012, 36226784801918510547852117, 292338319876651811428566992, 2009992643746035728869251645, 12045344786281525649136156960, 64072515057361294676198896292

Offset: 1

Marko Riedel, Nov 01 2018

nonn

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973.

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.

Cf. A002817, A321244, A321245.

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.

cp's OEIS Frontend

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

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