%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