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 A130840 a(n) = floor((1/16)*(16 + 2^n - 8*n + 8*n^2)). 1
 1, 1, 2, 4, 8, 13, 20, 30, 45, 69, 110, 184, 323, 591, 1116, 2154, 4217, 8329, 16538, 32940, 65727, 131283, 262376, 524542, 1048853, 2097453, 4194630, 8388960, 16777595, 33554839, 67109300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A face number function for a type of exceptional group expansion using Euler's formula V=E-F+2. Derived in Mathematica to give known exceptional group polyhedron sequence: (Platonic solids) e = n*(n - 1); v = f - 2^(n - 3); Solve[v + f - e - 2 == 0, f] Table[Round[{-e, v, f}], {n, 1, 7}] {{0, 1, 1}, {-2, 2, 2}, {-6, 4, 4}, {-12, 6, 8}, {-20, 9, 13}, {-30, 12, 20}, {-42, 14, 30}} Table[Apply[Plus, Round[{-e, v, f}]], {n, 1, 7}]->{2, 2, 2, 2, 2, 2, 2} This result is just a sequence of numbers that seem to work. LINKS MATHEMATICA Table[Round[(1/16)(16 + 2^n - 8 n + 8 n^2)], {n, 0, 30}] CROSSREFS Sequence in context: A173721 A247587 A061866 * A115266 A026039 A004978 Adjacent sequences:  A130837 A130838 A130839 * A130841 A130842 A130843 KEYWORD nonn AUTHOR Roger L. Bagula, Jul 19 2007 STATUS approved

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