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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.
2

%I #20 Mar 23 2024 21:30:18

%S 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,

%T 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,

%U 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

%N 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.

%C See A371254 for images of the graphs.

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

%e The table begins:

%e 0;

%e 0;

%e 0, 1;

%e 0;

%e 5, 5;

%e 0, 0, 0, 0, 1;

%e 49, 14;

%e 48, 8;

%e 171, 27, 0, 0, 0, 0, 0, 1;

%e 190, 20;

%e 484, 55;

%e 360, 12, 0, 0, 12, 0, 0, 0, 0, 0, 1;

%e 1027, 91;

%e 1078, 70;

%e 1830, 120, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0 1;

%e 2000, 112;

%e 3052, 204;

%e 3114, 90, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 5662, 285;

%e 5740, 240;

%e 8610, 378, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 8888, 330;

%e 12995, 506;

%e 12312, 336, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 18650, 650;

%e 18668, 572;

%e 25596, 810, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

%e \\ 0, 1;

%e 25928, 728;

%e 34887, 1015;

%e 32580, 510, 0, 0, 150, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

%e \\ 0, 0, 0, 0, 0, 1;

%e 46097, 1240;

%e 46464, 1120;

%e .

%e .

%Y Cf. A371254, A292105, A335102, A292104.

%K nonn,tabf

%O 1,6

%A _Scott R. Shannon_, Mar 18 2024