VOOZH about

URL: https://oeis.org/A289230

⇱ A289230 - OEIS

login
A289230
Number of nonequivalent ways to select 3 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.
5
0, 2, 19, 127, 536, 1688, 4357, 9789, 19844, 37172, 65397, 109335, 175214, 270934, 406329, 593463, 846934, 1184212, 1625979, 2196509, 2924050, 3841240, 4985531, 6399647, 8132044, 10237410, 12777167, 15820007, 19442436, 23729352, 28774625, 34681717, 41564304, 49546932
OFFSET
3,2
COMMENTS
Rotations and reflections of a selection are not counted. If they are to be counted see A289224.
LINKS
FORMULA
a(n) = (n^6 -6*n^5 -24*n^4 +220*n^3 -153*n^2 -1488*n +2592)/36 + IF(MOD(n, 2) = 1, -1)/2 + IF(MOD(n, 3) = 1, -2)/9.
G.f.: x^4*(2 + 9*x + 50*x^2 + 60*x^3 + 37*x^4 - 21*x^5 - 20*x^6 - 4*x^7 + 7*x^8) / ((1 - x)^7*(1 + x)*(1 + x + x^2)). - Colin Barker, Jun 30 2017
EXAMPLE
There are two nonequivalent ways to choose three 2 X 2 X 2 triangles (aaa, bbb, ccc) from a 4 X 4 X 4 point grid:
a a
a a a a
b c c b . c
b b c . b b c c
Note: aaa, bbb, ccc are not distinguishable, they are denoted differently for a better perception of the 2 X 2 X 2 triangles only.
PROG
(PARI) concat(0, Vec(x^4*(2 + 9*x + 50*x^2 + 60*x^3 + 37*x^4 - 21*x^5 - 20*x^6 - 4*x^7 + 7*x^8) / ((1 - x)^7*(1 + x)*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Jun 30 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Jun 30 2017
STATUS
approved