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A294522
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Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with diameter k (0<=k<n).
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7
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1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 14, 5, 1, 0, 1, 59, 43, 8, 1, 0, 1, 373, 387, 82, 9, 1, 0, 1, 4154, 5797, 1027, 125, 12, 1, 0, 1, 91518, 148229, 19320, 1818, 180, 13, 1, 0, 1, 4116896, 6959721, 598913, 37856, 2928, 239, 16, 1
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OFFSET
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1,9
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LINKS
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FORMULA
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a(n,1) = 1 for n > 1 (only K_n has diameter 1).
a(n,n-1) = 1 (only P_n has diameter n-1).
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 4, 1;
0, 1, 14, 5, 1;
0, 1, 59, 43, 8, 1;
0, 1, 373, 387, 82, 9, 1;
0, 1, 4154, 5797, 1027, 125, 12, 1;
...
a(2,1) = 1 since only P_2 has diameter 1.
a(3,1) = 1 since only C_3 has diameter 1.
a(3,2) = 1 since only P_3 has diameter 2.
a(4,1) = 1 since only K_4 has diameter 1.
a(4,2) = 4 since K_1,3, K4-e, the paw graph, and C_4 have diameter 2.
a(4,3) = 1 since only P_4 has diameter 3.
(End)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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