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A366479 Irregular triangle T(n,k) (n >= 0, k >= 2) read by rows. Consider the planar graph formed from an equilateral triangle with n equally spaced points placed on each edge, as discussed in A092867(n+1). Then T(n,k) is the number of interior points where exactly k chords cross.

%I A366479 #13 Nov 08 2023 07:52:06
%S A366479 0,3,1,42,7,123,37,6,444,90,6,3,1053,138,33,12,1,2145,285,63,15,0,3,
%T A366479 4173,481,72,24,12,6774,790,165,30,9,3,6,10698,1270,183,75,24,6,6,
%U A366479 16827,1584,393,102,6,12,6,3,25746,2220,339,135,40,12,6,6,35052,3084,684,177,42,18,6,9,6
%N A366479 Irregular triangle T(n,k) (n >= 0, k >= 2) read by rows. Consider the planar graph formed from an equilateral triangle with n equally spaced points placed on each edge, as discussed in A092867(n+1). Then T(n,k) is the number of interior points where exactly k chords cross.
%H A366479 Scott R. Shannon, <a href="/A366479/a366479.png">Image for n = 1</a>.
%H A366479 Scott R. Shannon, <a href="/A366479/a366479_1.png">Image for n = 2</a>.
%H A366479 Scott R. Shannon, <a href="/A366479/a366479_2.png">Image for n = 3</a>.
%H A366479 Scott R. Shannon, <a href="/A366479/a366479_3.png">Image for n = 4</a>.
%H A366479 Scott R. Shannon, <a href="/A366479/a366479_4.png">Image for n = 5</a>.
%H A366479 Scott R. Shannon, <a href="/A366479/a366479_5.png">Image for n = 10</a>.
%e A366479 Triangle begins:
%e A366479 0;
%e A366479 3, 1;
%e A366479 42, 7;
%e A366479 123, 37, 6;
%e A366479 444, 90, 6, 3;
%e A366479 1053, 138, 33, 12, 1;
%e A366479 2145, 285, 63, 15, 0, 3;
%e A366479 4173, 481, 72, 24, 12;
%e A366479 6774, 790, 165, 30, 9, 3, 6;
%e A366479 10698, 1270, 183, 75, 24, 6, 6;
%e A366479 16827, 1584, 393, 102, 6, 12, 6, 3;
%e A366479 25746, 2220, 339, 135, 40, 12, 6, 6;
%e A366479 35052, 3084, 684, 177, 42, 18, 6, 9, 6;
%e A366479 51378, 3667, 657, 237, 87, 30, 3, 0, 6;
%e A366479 67287, 5101, 1080, 255, 96, 21, 18, 15, 6;
%e A366479 87183, 6943, 1206, 393, 117, 57, 36, 24, 0, 0, 3;
%e A366479 113682, 8478, 1761, 486, 150, 27, 24, 30, 0, 15;
%e A366479 152460, 9927, 1557, 522, 180, 33, 51, 18, 12, 0, 1;
%e A366479 187131, 12585, 2559, 678, 180, 54, 24, 3, 24, 15, 6;
%e A366479 240942, 14190, 2358, 690, 318, 54, 42, 25, 12, 0, 15;
%e A366479 288459, 17866, 3372, 990, 342, 75, 48, 9, 36, 30, 0, 6;
%e A366479 ...
%Y A366479 Cf. A092867.
%Y A366479 See also A092866 (row sums), A366480 (T(n,2)/3).
%K A366479 nonn,tabf
%O A366479 0,2
%A A366479 _Scott R. Shannon_ and _N. J. A. Sloane_, Nov 07 2023