OFFSET
0,3
COMMENTS
Difference between the number of rows in the truth tables for circuit designs involving n variables and the order of S_n (the symmetric group on n symbols).
REFERENCES
Audu, M. S. and Ibrahim, A. A., (2006) Discrete Mathematics With Applications (in preparation)
Ibrahim, A. A., (2006) A stable Variety of Cayley Graphs For Efficient Interconnection Networks (submitted)
Ibrahim, A. A. and Audu, M. S., (2005) Some Group theoretic Properties of Certain class of (123) and (132)-avoiding patterns of certain numbers; An enumeration Scheme. African Journal of Natural Sciences, Afri. J. Nat. Sci., 8: 79-84.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..445
FORMULA
(-n+3)*a(n) +(n^2-n-4)*a(n-1) -2*(n-1)*(n-2)*a(n-2)=0 for n >= 3. - R. J. Mathar, Oct 20 2015; amended by Georg Fischer, Mar 13 2020
E.g.f.: 1/(1 - x) - exp(2*x). - G. C. Greubel, Oct 26 2017
MAPLE
f:= gfun:-rectoproc({(-n+3)*a(n) +(n^2-n-4)*a(n-1) -2*(n-1)*(n-2)*a(n-2)=0,
a(0)=0, a(1)=-1, a(2)=-2, a(3)=-2}, a(n), remember): map(f, [$0..40]); # Georg Fischer, Mar 13 2020
MATHEMATICA
Table[n!-2^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
PROG
(Sage) [factorial(n)-2^n for n in range(0, 23)] # Zerinvary Lajos, Oct 27 2009
(PARI) for(n=0, 25, print1(n!-2^n, ", ")) \\ G. C. Greubel, Oct 17 2017
(Magma) [Factorial(n)-2^n: n in [0..25]]; // G. C. Greubel, Oct 17 2017
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Aminu Alhaji Ibrahim, Oct 04 2006
STATUS
approved