A371264 Irregular triangle read by rows: T(n,k) is the number of internal vertices in the graph A371254(n) that are created by the crossing of k arcs, with k>=2.

0, 0, 0, 1, 0, 5, 5, 0, 0, 0, 0, 1, 49, 14, 48, 8, 171, 27, 0, 0, 0, 0, 0, 1, 190, 20, 484, 55, 360, 12, 0, 0, 12, 0, 0, 0, 0, 0, 1, 1027, 91, 1078, 70, 1830, 120, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2000, 112, 3052, 204, 3114, 90, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Scott R. Shannon, Mar 18 2024

Keywords

• nonn
• tabf

Comments

See A371254 for images of the graphs.

Examples

			The table begins:
0;
0;
0, 1;
0;
5, 5;
0, 0, 0, 0, 1;
49, 14;
48, 8;
171, 27, 0, 0, 0, 0, 0, 1;
190, 20;
484, 55;
360, 12, 0, 0, 12, 0, 0, 0, 0, 0, 1;
1027, 91;
1078, 70;
1830, 120, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0 1;
2000, 112;
3052, 204;
3114, 90, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
5662, 285;
5740, 240;
8610, 378, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
8888, 330;
12995, 506;
12312, 336, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
18650, 650;
18668, 572;
25596, 810, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                                                                        \\ 0,  1;
25928, 728;
34887, 1015;
32580, 510, 0, 0, 150, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                                                             \\ 0, 0, 0, 0, 0, 1;
46097, 1240;
46464, 1120;
.
.
		

Crossrefs

Cf. A371254, A292105, A335102, A292104.

Formula

Sum of row(n) = A371254(n) - n;