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A087698 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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