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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:
map(f, [$0..40]); # Robert Israel, Dec 05 2016
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).
Sequence in context: A029719 A347253 A039451 * A331766 A231971 A333279
KEYWORD
nonn
AUTHOR
Indranil Ghosh, Dec 05 2016
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)