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A221880
Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with exactly 1 fixed point.
6
1, 2, 8, 22, 57, 136, 315, 710, 1577, 3460, 7527, 16258, 34917, 74624, 158819, 336766, 711777, 1500028, 3152991, 6611834, 13835357, 28894072, 60234843, 125363062, 260512857, 540599156, 1120345175, 2318984050, 4794555477, 9902285680, 20430920787, 42114540398
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).
FORMULA
a(n) = A221878(n,1).
a(n) = A059570(n) + A221876(n,1) - n.
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