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A237529 Number of ways to choose 4 points in an n X n X n triangular grid so that no 3 of them form a 2 X 2 X 2 subtriangle.

%I A237529 #23 Sep 29 2019 14:02:13
%S A237529 6,156,1191,5565,19620,57351,146391,336951,714555,1417515,2660196,
%T A237529 4763226,8191911,13604220,21909810,34341666,52542036,78664446,
%U A237529 115493685,166585755,236429886,330634821,456141681,621465825,836970225,1115172981,1471091706,1922627616
%N A237529 Number of ways to choose 4 points in an n X n X n triangular grid so that no 3 of them form a 2 X 2 X 2 subtriangle.
%C A237529 All elements of the sequence are multiples of 3.
%H A237529 Heinrich Ludwig, <a href="/A237529/b237529.txt">Table of n, a(n) for n = 3..1000</a>
%H A237529 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A237529 a(n) = (n-1)*(n-2)*(n^6 + 7*n^5 + 13*n^4 - 7*n^3 - 230*n^2 - 408*n + 1152)/384.
%F A237529 G.f.: -3*x^3*(2*x^6 - 11*x^5 + 21*x^4 - 14*x^3 + x^2 + 34*x + 2) / (x-1)^9. - _Colin Barker_, Feb 09 2014
%t A237529 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{6,156,1191,5565,19620,57351,146391,336951,714555},40] (* _Harvey P. Dale_, Sep 29 2019 *)
%o A237529 (PARI) Vec(-3*x^3*(2*x^6-11*x^5+21*x^4-14*x^3+x^2+34*x+2)/(x-1)^9 + O(x^100)) \\ _Colin Barker_, Feb 09 2014
%Y A237529 Cf. A234251, A234250.
%K A237529 nonn,easy
%O A237529 3,1
%A A237529 _Heinrich Ludwig_, Feb 09 2014