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 A216175 Number of all polyhedra (tetrahedra of any orientation and octahedra) of any size, formed when intersecting a regular tetrahedron by planes parallel to its sides and dividing its edges into n equal parts. 3
 1, 6, 20, 50, 104, 193, 329, 526, 800, 1169, 1652, 2271, 3049, 4011, 5184, 6597, 8280, 10266, 12589, 15285, 18392, 21950, 26000, 30586, 35753, 41548, 48020, 55220, 63200, 72015, 81721, 92376, 104040, 116775, 130644, 145713, 162049, 179721, 198800, 219359 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,0,1,2,-3,1). FORMULA a(n) = (1/288)*(7+9*(-1)^n-16*(-1)^(n mod 3)+24*n+124*n^2+104*n^3+22*n^4). G.f.: x*(1+3*x+4*x^2+3*x^3)/((1+x)*(1+x+x^2)*(1-x)^5). - Bruno Berselli, Sep 11 2012 EXAMPLE For n=3, the number of tetrahedra of any orientation and size is t(3)+t(1)=15+1=16 and the number of octahedra of any size is t(2)=4 the total number being a(n)=20, where t(n) denotes the tetrahedral number A000292(n). MATHEMATICA Table[(1/288) (7 + 9 (-1)^n - 16 (-1)^Mod[n, 3] + 24 n + 124 n^2 + 104 n^3 + 22 n^4), {n, 50}] CROSSREFS Cf. A000292, A216172, A216173. Sequence in context: A299292 A162209 A161699 * A161409 A002415 A052515 Adjacent sequences:  A216172 A216173 A216174 * A216176 A216177 A216178 KEYWORD nonn,easy AUTHOR V.J. Pohjola, Sep 03 2012 STATUS approved

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Last modified October 23 12:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)