

A256120


Number of tautologies in propositional calculus of length n.


2



0, 0, 0, 0, 2, 2, 12, 6, 57, 88, 373, 554, 2198, 5413, 20397
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OFFSET

1,5


COMMENTS

a(n) is the number of tautologies that are n symbols long in propositional calculus with the connectives not (~), and (*), or (+), implies (>) and if and only if (<>).
When measuring the length of a tautology, all brackets must be included. The connectives > and <> are counted as one symbol each (but writing them as such requires nonASCII characters).
Formally, the language used for this sequence contains the symbols az and AZ (the variables),~,*,+,>,<>,( and ).
The formulas are defined by the following rules:
* Every variable is a formula.
* If A is a formula, then ~A is a formula.
* If A and B are formulas, then (A*B), (A+B), (A>B) and (A<>B) are all formulas.
A formula is a tautology if it is true for any assignment of truth values to the variables.


LINKS

Table of n, a(n) for n=1..15.
Matthew Scroggs, Logic Bot, pt. 2
Matthew Scroggs, List of tautologies


EXAMPLE

The tautologies of length 5 are (a>a) and (a<>a).
The tautologies of length 6 are (~a+a) and (a+~a).
The tautologies of length 7 are (~~a>a), (~~a<>a), (~a>~a), (~a<>~a), (a>~~a), (a<>~~a), ~(~a<>a), ~(~a*a), ~(a<>~a), ~(a*~a), ~~(a>a) and ~~(a<>a).


CROSSREFS

Cf. A277275, A277276
Sequence in context: A073768 A278534 A096855 * A024538 A279879 A279139
Adjacent sequences: A256117 A256118 A256119 * A256121 A256122 A256123


KEYWORD

nonn,more


AUTHOR

Matthew Scroggs, Mar 15 2015


EXTENSIONS

More terms from Matthew Scroggs, Mar 27 2015
Typo in a(11) corrected by Matthew Scroggs, Mar 27 2015
a(13) corrected, and a(14)a(15) added by Matthew Scroggs, Jul 02 2020


STATUS

approved



