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A331911
Triangle read by rows: Take an equilateral triangle with all diagonals drawn, as in A092867. Then T(n,k) = number of k-sided polygons in that figure for k = 3, 4, ..., n+2 and where n is the number of equal parts each side is divided into.
9
1, 12, 0, 48, 24, 3, 162, 90, 0, 0, 378, 306, 15, 16, 0, 774, 696, 84, 18, 0, 0, 1470, 1383, 219, 37, 0, 0, 0, 2604, 2382, 600, 78, 6, 6, 0, 0, 4224, 4089, 771, 177, 24, 6, 0, 0, 0, 6624, 6186, 1470, 234, 42, 0, 0, 0, 0, 0, 9738, 9486, 2307, 498, 48, 0, 0, 3, 0, 1, 0, 14010, 13548, 3984, 816, 144, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,2
EXAMPLE
An equilateral triangle with no other point along its edges, n = 1, contains 1 triangle so the first row is [1]. An equilateral triangle with 1 point dividing its edges, n = 2, contains 12 triangles and no other n-gons, so the second row is [12,0]. An equilateral triangle with 2 points dividing its edges, n = 3, contains 48 triangles, 24 quadrilaterals and 3 pentagons, so the third row is [48,24,3].
Triangle begins:
1
12,0
48,24,3
162,90,0,0
378,306,15,16,0
774,696,84,18,0,0
1470,1383,219,37,0,0,0
2604,2382,600,78,6,6,0,0
4224,4089,771,177,24,6,0,0,0
6624,6186,1470,234,42,0,0,0,0,0
9738,9486,2307,498,48,0,0,3,0,1,0
14010,13548,3984,816,144,0,0,0,0,0,0,0
19248,19224,5007,1102,156,18,0,0,0,0,0,0,0
26208,26142,8634,1668,192,24,0,0,0,0,0,0,0,0
The row sums are A092867.
KEYWORD
nonn,more,tabl
AUTHOR
STATUS
approved