|
|
A330302
|
|
Number of chains of 2-element subsets of {0,1, 2, ..., n} that contain no consecutive integers.
|
|
8
|
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
For n >= 1, a(n) is the number of chains of binary reflexive symmetric matrices of order n.
The number of chains of strictly upper triangular or strictly lower triangular matrices.
Also, number of chains in power set of (n^2-n)/2 elements.
a(n) is the number of distinct reflexive symmetric fuzzy matrices of order n.
|
|
LINKS
|
V. Murali and B. Makamba, Finite Fuzzy Sets, Int. J. Gen. Syst., Vol. 34 (1) (2005), pp. 61-75.
|
|
FORMULA
|
|
|
MAPLE
|
# P are the polynomials defined in A007047.
a:= n -> (m-> 2^m*subs(x=1/2, P(m, x)))(n*(n-1)/2):
seq(a(n), n=0..9);
# second Maple program:
b:= proc(n) option remember; `if`(n=0, 4,
add(b(n-j)*binomial(n, j), j=1..n))
end:
a:= n-> `if`(n<2, 1, b(n*(n-1)/2)-1):
|
|
MATHEMATICA
|
Array[2 PolyLog[-(#^2-#)/2, 1/2] - 1 &, 10, 0]
Table[2*PolyLog[-(n^2-n)/2, 1/2] - 1, {n, 0, 29}]
Table[LerchPhi[1/2, -(n^2-n)/2, 2]/2, {n, 0, 19}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|