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A367432
Number of commutative discrete aggregation functions defined on the finite chain L_n={0,1,...,n-1,n} that are smooth.
1
1, 2, 10, 80, 1008, 19764, 600028, 28134464, 2034669118, 226781039624
OFFSET
0,2
COMMENTS
The number of smooth and commutative discrete aggregation functions on the finite chain L_n={0,1,...,n-1,n}, i.e., the number of monotonic increasing binary functions F: L_n^2->L_n such that F(0,0)=0 and F(n,n)=n, F(x,y)=F(y,x) for all x,y in L_n (commutativity), and F(x+1,y)-F(x,y)<=1 and F(y,x+1)-F(y,x)<=1 for all y in L_n and x in L_n\{n} (smooth).
Also, the number of (n+1)X(n+1) integer symmetric matrices (m_{i,j}) such that m_{1,1}=1, m_{n+1,n+1}=n+1, and all rows and columns are (weakly) monotonic without jumps larger than 1.
CROSSREFS
Symmetric counterpart of matrices enumerated in A306372.
Smooth counterpart of operators defined in A366447.
Sequence in context: A064312 A063902 A088351 * A231919 A174962 A062396
KEYWORD
nonn,hard,more
AUTHOR
Marc Munar, Nov 18 2023
EXTENSIONS
a(0) and a(7)-a(9) from Martin Ehrenstein, Dec 01 2023
STATUS
approved