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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..40.

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