|
| |
|
|
A321587
|
|
Number of (0,1)-matrices with n ones, no zero rows or columns, and distinct rows.
|
|
6
|
|
|
|
1, 1, 3, 17, 129, 1227, 14123, 190265, 2934359, 50975647, 984801759, 20941104299, 486007744671, 12223797601887, 331190083773701, 9616356919931711, 297887922137531747, 9805965265937326129, 341827167387114704421, 12579123760272833723975, 487315396984696657840761
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Also number of colored compositions of n using all colors of an initial interval of the color palette such that all parts have different color patterns and the patterns for parts i have i distinct colors in increasing order. a(3) = 17: 2ab1a, 2ab1b, 1a2ab, 1b2ab, 3abc, 2ab1c, 2ac1b, 2bc1a, 1a2bc, 1b2ac, 1c2ab, 1a1b1c, 1a1c1b, 1b1a1c, 1b1c1a, 1c1a1b, 1c1b1a. - Alois P. Heinz, Sep 17 2019
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) ~ c * d^n * n!, where d = 1.938593839617140963759657977... and c = 0.350862127201784401195038... - Vaclav Kotesovec, Feb 05 2022
|
|
|
EXAMPLE
|
The a(3) = 17 matrices:
[1 1 1]
.
[1 1] [1 1] [1 1 0] [1 0 1] [1 0] [1 0 0] [0 1 1] [0 1] [0 1 0] [0 0 1]
[1 0] [0 1] [0 0 1] [0 1 0] [1 1] [0 1 1] [1 0 0] [1 1] [1 0 1] [1 1 0]
.
[1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
[0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
[0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
|
|
|
MAPLE
|
C:= binomial:
b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
b(n-i*j, min(n-i*j, i-1), k, p+j)*C(C(k, i), j), j=0..n/i)))
end:
a:= n-> add(add(b(n$2, i, 0)*(-1)^(k-i)*C(k, i), i=0..k), k=0..n):
|
|
|
MATHEMATICA
|
prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];
Table[Length[Select[Subsets[Tuples[Range[n], 2], {n}], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], UnsameQ@@prs2mat[#]]&]], {n, 5}]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
