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 A282819 Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no two opposite edges have the same color. 2
 0, 0, 2, 22, 152, 680, 2270, 6202, 14672, 31152, 60810, 110990, 191752, 316472, 502502, 771890, 1152160, 1677152, 2387922, 3333702, 4572920, 6174280, 8217902, 10796522, 14016752, 18000400, 22885850, 28829502, 36007272, 44616152, 54875830, 67030370, 81349952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..32. 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)/12. G.f.: -2*x^2*(1+4*x+20*x^2+4*x^3+x^4) / (x-1)^7 . - R. J. Mathar, Feb 23 2017 a(n) = 2*A282816(n). - R. J. Mathar, Feb 23 2017 EXAMPLE For n = 2 we get a(2) = 2 distinct ways to color the edges of a tetrahedron in two colors so that no two opposite edges have the same color. MATHEMATICA Table[(n - 1) n (n^4 - 2 n^3 + n^2 + 8)/12, {n, 0, 33}] PROG (PARI) a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/12 \\ Charles R Greathouse IV, Feb 22 2017 CROSSREFS Cf. A282816, A282818, A282820. A046023 (tetrahedral edge colorings without restriction). Sequence in context: A082940 A286778 A232977 * A123960 A265864 A091169 Adjacent sequences: A282816 A282817 A282818 * A282820 A282821 A282822 KEYWORD nonn,easy AUTHOR David Nacin, Feb 22 2017 STATUS approved

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Last modified June 25 02:21 EDT 2024. Contains 373691 sequences. (Running on oeis4.)