login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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