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Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=2, formed when n equally spaced points are placed around a circle and all pairs of points are joined by an interior arc whose radius equals the circle's radius.
4

%I #13 Mar 23 2024 21:21:04

%S 1,3,3,4,0,1,10,10,5,1,12,6,14,56,21,0,7,1,8,48,32,0,0,0,1,27,144,54,

%T 27,18,10,160,70,0,30,0,0,0,1,22,253,330,11,33,0,0,0,0,1,12,276,204,0,

%U 24,26,624,403,130,104,0,0,0,0,0,0,1,14,630,448,112,70,14,14,0,0,0,0,0,1,45,960,915,165,165

%N Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=2, formed when n equally spaced points are placed around a circle and all pairs of points are joined by an interior arc whose radius equals the circle's radius.

%C See A371253 and A371254 for images.

%F Sum of row n = A371253(n).

%e The table begins:

%e 1;

%e 3, 3;

%e 4, 0, 1;

%e 10, 10, 5, 1;

%e 12, 6;

%e 14, 56, 21, 0, 7, 1;

%e 8, 48, 32, 0, 0, 0, 1;

%e 27, 144, 54, 27, 18;

%e 10, 160, 70, 0, 30, 0, 0, 0, 1;

%e 22, 253, 330, 11, 33, 0, 0, 0, 0, 1;

%e 12, 276, 204, 0, 24;

%e 26, 624, 403, 130, 104, 0, 0, 0, 0, 0, 0, 1;

%e 14, 630, 448, 112, 70, 14, 14, 0, 0, 0, 0, 0, 1;

%e 45, 960, 915, 165, 165;

%e 16, 1136, 704, 272, 192, 0, 16, 0, 0, 0, 0, 0, 0, 0, 1;

%e 34, 1581, 1870, 238, 272, 17, 34, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 18, 1656, 1386, 270, 288, 0, 18;

%e 38, 2622, 2546, 646, 513, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 20, 2680, 2420, 820, 380, 20, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 63, 3297, 4725, 1050, 315, 42, 105;

%e 22, 3696, 4136, 1342, 484, 22, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%Y Cf. A371253 (regions), A371254 (vertices), A371255 (edges), A331450, A359009, A359061, A359258.

%K nonn,tabf

%O 2,2

%A _Scott R. Shannon_, Mar 17 2024