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.

0, 3, 1, 42, 7, 123, 37, 6, 444, 90, 6, 3, 1053, 138, 33, 12, 1, 2145, 285, 63, 15, 0, 3, 4173, 481, 72, 24, 12, 6774, 790, 165, 30, 9, 3, 6, 10698, 1270, 183, 75, 24, 6, 6, 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

Offset

0,2

Links

Table of n, a(n) for n=0..66.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 10.

Example

Triangle begins:
0;
3, 1;
42, 7;
123, 37, 6;
444, 90, 6, 3;
1053, 138, 33, 12, 1;
2145, 285, 63, 15, 0, 3;
4173, 481, 72, 24, 12;
6774, 790, 165, 30, 9, 3, 6;
10698, 1270, 183, 75, 24, 6, 6;
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;
51378, 3667, 657, 237, 87, 30, 3, 0, 6;
67287, 5101, 1080, 255, 96, 21, 18, 15, 6;
87183, 6943, 1206, 393, 117, 57, 36, 24, 0, 0, 3;
113682, 8478, 1761, 486, 150, 27, 24, 30, 0, 15;
152460, 9927, 1557, 522, 180, 33, 51, 18, 12, 0, 1;
187131, 12585, 2559, 678, 180, 54, 24, 3, 24, 15, 6;
240942, 14190, 2358, 690, 318, 54, 42, 25, 12, 0, 15;
288459, 17866, 3372, 990, 342, 75, 48, 9, 36, 30, 0, 6;
...

Crossrefs

Cf. A092867.

See also A092866 (row sums), A366480 (T(n,2)/3).

Sequence in context: A356819 A362166 A136517 * A104097 A344379 A155812

Adjacent sequences: A366476 A366477 A366478 * A366480 A366481 A366482

Keyword

nonn,tabf

Author

Scott R. Shannon and N. J. A. Sloane, Nov 07 2023

Status

approved