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A289226 Number of ways to select 5 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.

%I A289226 #8 Jul 01 2017 13:16:17
%S A289226 0,420,15108,190371,1336320,6528948,24951780,79851975,223419840,
%T A289226 562591836,1301255556,2806131075,5705746752,11034449244,20436317412,
%U A289226 36447218199,62877079680,105318792564,171815016708,273719593923,426796282752,652604165220,980226360036,1448406641607
%N A289226 Number of ways to select 5 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.
%C A289226 Rotations and reflections of a selection are regarded as different. For the number of congruence classes see A289232.
%H A289226 Heinrich Ludwig, <a href="/A289226/b289226.txt">Table of n, a(n) for n = 5..100</a>
%H A289226 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A289226 a(n) = (n^10 -10*n^9 -85*n^8 +1160*n^7 +1345*n^6 -49162*n^5 +62145*n^4 +892140*n^3 -2198566*n^2 -5725008*n +18190440)/120.
%F A289226 G.f.: 3*x^6*(140 + 3496*x + 15761*x^2 + 1293*x^3 - 18129*x^4 + 3779*x^5 + 6103*x^6 - 1637*x^7 - 1139*x^8 + 413*x^9) / (1 - x)^11. - _Colin Barker_, Jul 01 2017
%e A289226 There are 420 ways to choose five 2 X 2 X 2 triangles (aaa, ..., eee) from a 6 X 6 X 6 point grid, for example:
%e A289226         .               a
%e A289226        . .             a a
%e A289226       . . .           . d .
%e A289226      a a b b         b d d c
%e A289226     c a d b e       b b e c c
%e A289226    c c d d e e     . . e e . .
%e A289226 Note: aaa, ..., eee are not distinguishable, they are denoted differently for a better perception of the 2 X 2 X 2 triangles only.
%o A289226 (PARI) concat(0, Vec(3*x^6*(140 + 3496*x + 15761*x^2 + 1293*x^3 - 18129*x^4 + 3779*x^5 + 6103*x^6 - 1637*x^7 - 1139*x^8 + 413*x^9) / (1 - x)^11 + O(x^40))) \\ _Colin Barker_, Jul 01 2017
%Y A289226 Cf. A289222, A289223, A289224, A289225, A289227, A289228, A289232.
%K A289226 nonn,easy
%O A289226 5,2
%A A289226 _Heinrich Ludwig_, Jul 01 2017