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 A321244 Non-isomorphic proper colorings of the 3 X 3 grid graph using at most n colors under rotational and reflectional symmetries. 3
 0, 2, 69, 1572, 19865, 153480, 830802, 3476144, 12003462, 35757630, 94780235, 228579252, 509929719, 1065625652, 2106541920, 3969848640, 7176749852, 12509692794, 21113614017, 34626453860, 55344881445, 86431928352, 132174030494, 198295824432, 292341936450, 424135940150, 606327641127, 855040875444, 1190635082147, 1638595028940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 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. Marko Riedel, Maple code for OCP computation by Burnside. Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA a(n) = (1/8)*n^9 - (3/2)*n^8 + (33/4)*n^7 - (53/2)*n^6 + (217/4)*n^5 - (291/4)*n^4 + (507/8)*n^3 - (133/4)*n^2 + 8*n. From Colin Barker, Nov 01 2018: (Start) G.f.: x^2*(2 + 49*x + 972*x^2 + 7010*x^3 + 17710*x^4 + 15273*x^5 + 4076*x^6 + 268*x^7) / (1 - x)^10. a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10. (End) MATHEMATICA CoefficientList[Series[x (2 + 49 x + 972 x^2 + 7010 x^3 + 17710 x^4 + 15273 x^5 + 4076 x^6 + 268 x^7) / (1 - x)^10, {x, 0, 30}], x] (* Vincenzo Librandi Nov 04 2018 *) PROG (PARI) concat(0, Vec(x^2*(2 + 49*x + 972*x^2 + 7010*x^3 + 17710*x^4 + 15273*x^5 + 4076*x^6 + 268*x^7) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Nov 01 2018 (Magma) [(1/8)*n^9-(3/2)*n^8+(33/4)*n^7-(53/2)*n^6+(217/4)*n^5-(291/4)*n^4 +(507/8)*n^3-(133/4)*n^2+8*n: n in [1..30]]; // Vincenzo Librandi, Nov 04 2018 CROSSREFS Cf. A002817, A321245, A321246. Sequence in context: A362291 A041577 A180085 * A224506 A085915 A285217 Adjacent sequences: A321241 A321242 A321243 * A321245 A321246 A321247 KEYWORD nonn,easy AUTHOR Marko Riedel, Nov 01 2018 STATUS approved

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Last modified June 10 04:13 EDT 2023. Contains 363187 sequences. (Running on oeis4.)