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A123474
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Triangle read by rows: T(n,k) = number of labeled bicolored nonseparable graphs with k points in one color class and n-k points in the other class. The classes are interchangeable if k = n-k. Here n >= 2, k=1..n-1.
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3
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1, 0, 0, 0, 3, 0, 0, 10, 10, 0, 0, 15, 340, 15, 0, 0, 21, 6965, 6965, 21, 0, 0, 28, 51296, 246295, 51296, 28, 0, 0, 36, 326676, 14750946, 14750946, 326676, 36, 0, 0, 45, 1917840, 322476210, 796058676, 322476210, 1917840, 45, 0, 0, 55, 10683255
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OFFSET
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2,5
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REFERENCES
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R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
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LINKS
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FORMULA
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T(n,k) = f(n-2*k) * binomial(n,k) * A123301(n, k) where f(0) = 1/2 and 1 otherwise.
A004100(n) = Sum_{k=0..floor(n/2)} T(n,k). (End)
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EXAMPLE
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Triangle begins:
1;
0, 0;
0, 3, 0;
0, 10, 10, 0;
0, 15, 340, 15, 0;
0, 21, 6965, 6965, 21, 0;
0, 28, 51296, 246295, 51296, 28, 0;
...
Formatted as an array:
==========================================================
m/n | 1 2 3 4 5 6
----+-----------------------------------------------------
1 | 1 0 0 0 0 0 ...
2 | 0 3 10 15 21 28 ...
3 | 0 10 340 6965 51296 326676 ...
4 | 0 15 6965 246295 14750946 322476210 ...
5 | 0 21 51296 14750946 796058676 105725374062 ...
6 | 0 28 326676 322476210 105725374062 9736032295374 ...
...
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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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