OFFSET
1,2
REFERENCES
A. D. Adeshola, V. Maltcev, and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, (submitted 2013).
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-7,-1,8,-4).
FORMULA
a(n) = A221878(n,1).
G.f.: x*(1-3*x+5*x^2-3*x^3-3*x^4+x^5)/((1+x)*(1-3*x+2*x^2)^2). [Bruno Berselli, Mar 01 2013]
a(n) = -n+(2^(n-1)*(21*n+34)-8*(-1)^n)/36 for n>1, a(1)=1. [Bruno Berselli, Mar 01 2013]
EXAMPLE
a(3) = 8 because there are exactly 8 order-preserving or order-reversing full contraction mappings (of a 3-chain) with exactly 1 fixed point, namely: (111), (112), (222), (233), (333), (321), (322), (221).
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Abdullahi Umar, Feb 28 2013
EXTENSIONS
More terms from Bruno Berselli, Mar 01 2013
STATUS
approved