A334691 Irregular triangle read by rows: T(n,k) (n >= 1, 2 <= k <= 2*n) = number of interior vertices in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter) where k lines meet.

1, 20, 8, 1, 204, 32, 8, 0, 1, 616, 152, 20, 8, 4, 0, 1, 2428, 252, 36, 16, 4, 0, 0, 0, 1, 3968, 572, 156, 72, 16, 8, 4, 0, 4, 0, 1, 11164, 900, 120, 52, 16, 8, 4, 0, 0, 0, 0, 0, 1, 16884, 1712, 396, 132, 40, 20, 8, 8, 8, 0, 0, 0, 0, 0, 1, 30116, 2536, 600, 140, 60, 24, 8, 20, 8, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, May 18 2020

Keywords

• nonn
• tabf

Comments

No formula is known.

Examples

			Triangle begins:
1;
20,8,1;
204,32,8,0,1;
616,152,20,8,4,0,1;
2428,252,36,16,4,0,0,0,1;
3968,572,156,72,16,8,4,0,4,0,1;
11164,900,120,52,16,8,4,0,0,0,0,0,1;
16884,1712,396,132,40,20,8,8,8,0,0,0,0,0,1;
30116,2536,600,140,60,24,8,20,8,0,0,0,0,0,0,0,1;
43988,4056,948,312,84,56,52,20,,8,0,0,4,0,0,0,0,0,1;
82016,4660,580,228,48,84,4,4,4,8,4,0,0,0,0,0,0,0,0,0,1;
90088,8504,1840,780,424,128,68,32,32,0,0,8,24,0,0,0,4,0,0,0,0,0,1;
168360,8284,1056,396,128,100,52,12,4,4,4,8,4,0,0,0,0,0,0,0,0,0,0,0,1;
202332,13144,2980,924,256,144,140,60,44,4,0,8,8,8,0,0,4,0,0,0,0,0,0,0,0,0,1;
...
		

Links

• Scott R. Shannon, Data for triangles A334691 and A334699
• Scott R. Shannon, Colored illustration for n = 2
• Scott R. Shannon, Illustration for n=3 showing interior vertices color-coded according to multiplicity.

Crossrefs

Cf. A255011, A331449, A334690 (row sums), A334692 (column k=2), A334693 (k=3), A334694-A334699.