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Number of contradictions in propositional calculus of length n.
2

%I #22 Oct 11 2016 04:56:34

%S 0,0,0,0,0,6,2,20,6,127,154

%N Number of contradictions in propositional calculus of length n.

%C a(n) is the number of contradictions that are n symbols long in propositional calculus with the connectives not (~), and (*), or (+), implies (->) and if and only if (<->).

%C When measuring the length of a contradiction, all brackets must be included. The connectives -> and <-> are counted as one symbol each (but writing them as such requires non-ASCII characters).

%C Formally, the language used for this sequence contains the symbols a-z and A-Z (the variables), ~, *, +, ->, <->, ( and ).

%C The formulas are defined by the following rules:

%C - every variable is a formula;

%C - if A is a formula, then ~A is a formula;

%C - if A and B are formulas, then (A*B), (A+B), (A->B) and (A<->B) are all formulas.

%C A formula is a contradiction if it is false for any assignment of truth values to the variables.

%H M. Scroggs, <a href="http://mscroggs.co.uk/blog/35">Logical Contradictions</a>

%H M. Scroggs, <a href="http://www.mscroggs.co.uk/blog/contradictions.txt">List of contradictions</a>

%e There are 6 contradictions of length 6: ~(a<->a), ~(a->a), (~a*a), (~a<->a), (a*~a) and (a<->~a), so a(6)=6.

%e There are 2 contradictions of length 7: ~(~a+a) and ~(a+~a), so a(7)=2.

%Y Cf. A256120, A277276.

%K nonn,more

%O 1,6

%A _Matthew Scroggs_, Oct 08 2016