This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A230723 #39 Oct 24 2020 19:02:14
%S A230723 0,1,6,25,87,238,575,1228,2425,4446,7734,12806,20422,31444,47072,
%T A230723 68639,97929,136893,188061,254170,338679,445297,578616,743524,945968,
%U A230723 1192243,1489894,1846869,2272575,2776880,3371335,4068016,4880921,5824640,6915942,8172258,9613470
%N A230723 Number of non-equivalent ways to choose three points in an equilateral triangle grid of side n.
%H A230723 Heinrich Ludwig, <a href="/A230723/b230723.txt">Table of n, a(n) for n = 1..1000</a>
%H A230723 <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 A230723 a(n) = (n^6 + 3*n^5 - 3*n^4 + 10*n^3 + B + C)/288
%F A230723 where
%F A230723 B = 27*n^2 + 3*n - 9 if n odd
%F A230723 B = 48*n otherwise
%F A230723 and
%F A230723 C = -32 if n == 1 (mod 3)
%F A230723 C = 0 otherwise
%F A230723 G.f.: x^2*(1 + 3*x + 7*x^2 + 19*x^3 + 16*x^4 + 12*x^5 + x^6 + 2*x^7 - x^8)/((1-x^3) * (1-x^2)^3 * (1-x)^3). - _Ralf Stephan_, Nov 03 2013
%e A230723 for n = 3 there are the following a(3) = 6 choices of 3 points (=X) (rotations and reflections ignored):
%e A230723 X . . X . X
%e A230723 . . X X . . X X . X X .
%e A230723 X . X . X . X X X . . . X . X . X .
%t A230723 LinearRecurrence[{3,0,-7,3,6,0,-6,-3,7,0,-3,1},{0,1,6,25,87,238,575,1228,2425,4446,7734,12806},40] (* _Harvey P. Dale_, Oct 24 2020 *)
%Y A230723 Cf. A001399, A014409, A082966, A227327.
%K A230723 nonn,easy
%O A230723 1,3
%A A230723 _Heinrich Ludwig_, Oct 28 2013