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A087698
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Triangle read by rows, giving T(n,k) = maximum number of examples (Boolean inputs) at Hamming distance 2 for symmetric Boolean functions that can have different outputs.
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2
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1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 4, 4, 3, 1, 1, 4, 7, 8, 7, 4, 1, 1, 5, 11, 15, 15, 11, 5, 1, 1, 6, 16, 26, 30, 26, 16, 6, 1, 1, 7, 22, 42, 56, 56, 42, 22, 7, 1, 1, 8, 29, 64, 98, 112, 98, 64, 29, 8, 1, 1, 9, 37, 93, 162, 210, 210, 162, 93, 37, 9, 1, 1, 10, 46, 130, 255, 372, 420
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| This sets an upper bound on the second order term of the complexity measure introduced by Franco, 2001 for symmetric Boolean functions. The sum of the terms for a given N is equal to 2^(N-1).
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LINKS
| Franco, L., A measure for the complexity of Boolean functions ...
Franco, L. and Cannas, S. A., Non-glassy ground-state in a long-range antiferromagnetic frustrated model in the hypercubic cell, Phys. A 332 (2004), no. 1-4, 337-348.
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FORMULA
| T(n, N) = ((N-n)^2 + n^2 - N) * C(N, n) / (N^2 - N) n is the term for the series containing N+1 terms
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EXAMPLE
| Triangle begins:
1 N=0
1 1 N=1
1 0 1 N=2
1 1 1 1 N=3
1 2 2 2 1 N=4
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CROSSREFS
| Cf. A088219.
Sequence in context: A162246 A118400 A159853 * A101677 A152067 A193884
Adjacent sequences: A087695 A087696 A087697 * A087699 A087700 A087701
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KEYWORD
| nonn,tabl
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AUTHOR
| Leonardo Franco (Leonardo.Franco(AT)psy.ox.ac.uk), Sep 24 2003
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