login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A277276 Number of tautologies and contradictions in propositional calculus of length n. 2
0, 0, 0, 0, 2, 8, 14, 26, 63, 215, 527 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
a(n) is the number of tautologies and contradictions 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 formula all brackets must be included. The connectives -> and <-> are counted as one symbol each (but writing them as such requires non-ASCII characters).
Formally, the language used for this sequence contains the symbols a-z and A-Z (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.
A formula is a contradiction if it is false for any assignment of truth values to the variables.
This sequence is increasing, as adding a ~ to the start of a tautology or contradiction gives a contradiction or tautology one symbol longer.
LINKS
EXAMPLE
The contradictions of length 6 are ~(a<->a), ~(a->a), (~a*a), (~a<->a), (a*~a) and (a<->~a): 6 formulas, and the tautologies of length 6 are (~a+a) and (a+~a): 2 formulas. So a(6) = 6+2 = 8.
CROSSREFS
Equals A256120 plus A277275
Sequence in context: A161156 A125902 A295055 * A324785 A173974 A056677
KEYWORD
nonn,more
AUTHOR
Matthew Scroggs, Oct 08 2016
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)