A237530 - OEIS

%I #21 Dec 09 2021 14:59:35

%S 0,4,22,82,231,566,1216,2410,4428,7712,12780,20392,31409,47032,68594,

%T 97878,136836,187998,254100,338602,445213,578524,743424,945860,

%U 1192126,1489768,1846734,2272430,2776725,3371170,4067840,4880734,5824442,6915732,8172036,9613236

%N Number of non-equivalent (mod D_3) ways to choose three points in an n X n X n triangular grid so that they do not form a 2 X 2 X 2 subtriangle.

%C Without the restriction "non-equivalent (mod D_3)" the numbers are given by A234250.

%H Heinrich Ludwig, <a href="/A237530/b237530.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-7,3,6,0,-6,-3,7,0,-3,1)

%F a(n) = (n^6 + 3*n^5 - 3*n^4 + 10*n^3 - 48*n^2 + IF(n==1 mod 2)*(27*n^2 - 45*n - 9) + IF(n==1 mod 3)*64)/288.

%F G.f.: x^3*(x^7-x^6-2*x^5-15*x^4-13*x^3-16*x^2-10*x-4) / ((x-1)^7*(x+1)^3*(x^2+x+1)). - _Colin Barker_, Feb 14 2014

%t LinearRecurrence[{3,0,-7,3,6,0,-6,-3,7,0,-3,1},{0,4,22,82,231,566,1216,2410,4428,7712,12780,20392},40] (* _Harvey P. Dale_, Dec 09 2021 *)

%Y Cf. A234250, A234247.

%K nonn,easy

%O 2,2

%A _Heinrich Ludwig_, Feb 13 2014