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 A282816 Number of inequivalent ways to color the faces of a cube using at most n colors so that no two opposite sides have the same color. 2
 0, 0, 1, 11, 76, 340, 1135, 3101, 7336, 15576, 30405, 55495, 95876, 158236, 251251, 385945, 576080, 838576, 1193961, 1666851, 2286460, 3087140, 4108951, 5398261, 7008376, 9000200, 11442925, 14414751, 18003636, 22308076, 27437915, 33515185, 40674976, 49066336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also the number of inequivalent ways to color the corners of an octahedron using at most n colors so that no two opposite corners have the same color. LINKS Table of n, a(n) for n=0..33. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/24. G.f.: -x^2*(1+4*x+20*x^2+4*x^3+x^4)/(x-1)^7 . - R. J. Mathar, Feb 23 2017 EXAMPLE For n = 2 we get a(2) = 1 way to color the faces of a cube with two colors so that no two opposite sides have the same color. MATHEMATICA Table[(8n(n-1) + n^3(n-1)^3) /24, {n, 0, 35}] PROG (PARI) a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/24 \\ Charles R Greathouse IV, Feb 22 2017 CROSSREFS Cf. A282817, A047780 (face colorings without restriction). Sequence in context: A287330 A282384 A092225 * A055901 A036427 A122589 Adjacent sequences: A282813 A282814 A282815 * A282817 A282818 A282819 KEYWORD nonn,easy AUTHOR David Nacin, Feb 21 2017 STATUS approved

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Last modified February 22 13:32 EST 2024. Contains 370255 sequences. (Running on oeis4.)