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A283417
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Number T(n,k) of triangle-free graphs on n unlabeled nodes with exactly k connected components; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
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3
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1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 3, 2, 1, 1, 0, 6, 4, 2, 1, 1, 0, 19, 10, 5, 2, 1, 1, 0, 59, 28, 11, 5, 2, 1, 1, 0, 267, 90, 32, 12, 5, 2, 1, 1, 0, 1380, 363, 100, 33, 12, 5, 2, 1, 1, 0, 9832, 1784, 397, 104, 34, 12, 5, 2, 1, 1, 0, 90842, 11770, 1892, 407, 105, 34, 12, 5, 2, 1, 1
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OFFSET
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0,12
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LINKS
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Alois P. Heinz, Rows n = 0..17, flattened
Index entries for triangles generated by the Multiset Transformation
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FORMULA
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G.f.: Product_{j>=1} 1/(1-y*x^j)^A024607(j).
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EXAMPLE
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Triangle T(n,k) begins:
1;
0, 1;
0, 1, 1;
0, 1, 1, 1;
0, 3, 2, 1, 1;
0, 6, 4, 2, 1, 1;
0, 19, 10, 5, 2, 1, 1;
0, 59, 28, 11, 5, 2, 1, 1;
0, 267, 90, 32, 12, 5, 2, 1, 1;
0, 1380, 363, 100, 33, 12, 5, 2, 1, 1;
0, 9832, 1784, 397, 104, 34, 12, 5, 2, 1, 1;
...
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CROSSREFS
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Columns k=0-1 give: A000007, A024607.
Row sums give A006785.
Sequence in context: A287576 A035103 A155033 * A107889 A138384 A129172
Adjacent sequences: A283414 A283415 A283416 * A283418 A283419 A283420
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz, Apr 14 2017
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STATUS
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approved
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