id:A087698 - OEIS Search Results

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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.

+0
3

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; listen)

	OFFSET	`0,12`
	COMMENT	`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).`
	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.`
	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`
	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`
	CROSSREFS	`Cf. A088219.` `Sequence in context: A162246 A118400 A159853 this_sequence A101677 A152067 A128084` `Adjacent sequences: A087695 A087696 A087697 this_sequence A087699 A087700 A087701`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Leonardo Franco (Leonardo.Franco(AT)psy.ox.ac.uk), Sep 24 2003`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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