cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A064436 Number of switching functions of n or fewer variables which cannot be realized as threshold gates.

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%I A064436 #9 Sep 05 2017 03:11:37
%S A064436 0,0,2,152,63654,4294872724,18446744073694523482,
%T A064436 340282366920938463463374607423390140592,
%U A064436 115792089237316195423570985008687907853269984665640564039457583990351590086990
%N A064436 Number of switching functions of n or fewer variables which cannot be realized as threshold gates.
%C A064436 The corresponding systems of linear inequalities are not solvable: linearly non-separable truth or switching functions. Truth functions which ar "non-neurons" and are realizable only as two levels threshold gate networks.
%H A064436 Wang Lan, <a href="/A064436/b064436.txt">Table of n, a(n) for n = 0..9</a>
%F A064436 a(n) = 2^(2^n) - A000609(n).
%e A064436 n=2: out of the 16 B^2 -> B^1 truth functions, 14 are linearly separable; the 2 exceptions are XOR and its negation: f(x,y) = !xz + x!y and !f(x,y) = xy + !x!y. So a(2)=2. With increasing n, the chance that a switching function belongs to this sequence tends to 1.
%Y A064436 Cf. A000609.
%K A064436 nonn
%O A064436 0,3
%A A064436 _Labos Elemer_, Oct 01 2001