|
|
A279063
|
|
Number of 2 X 2 matrices having entries in {0,1,...,n} and determinant in the closed interval [-n,n] with no entry repeated.
|
|
1
|
|
|
0, 0, 0, 16, 56, 136, 296, 512, 864, 1280, 1912, 2616, 3680, 4760, 6200, 7848, 9792, 11832, 14632, 17280, 20784, 24352, 28480, 32584, 38200, 43168, 49160, 55472, 62936, 69784, 79008, 86944, 96952, 106816, 117672, 128592, 142352, 154088, 167968
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
a(n) mod 8 = 0.
|
|
LINKS
|
|
|
MAPLE
|
f:= proc(n) local C;
C:= combinat:-choose([$0..n], 4);
C:= map(t -> (t[1]*t[2]-t[3]*t[4], t[1]*t[3]-t[2]*t[4], t[1]*t[4]-t[2]*t[3]), C);
8*nops(select(t -> abs(t)<=n, C))
end proc:
|
|
PROG
|
(Python)
def t(n):
s=0
for a in range(0, n+1):
for b in range(0, n+1):
for c in range(0, n+1):
for d in range(0, n+1):
if (a!=b and a!=d and b!=d and c!=a and c!=b and c!=d):
if (a*d-b*c) in range(-n, n+1):
s+=1
return s
for i in range(0, 151):
print str(i)+" "+str(t(i))
|
|
CROSSREFS
|
Cf. A211031 (where in the entries can be repeated).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|