

A278846


Number of unimodular 2 X 2 matrices having entries in {0,1,...,n} with no entry repeated.


2



0, 0, 0, 0, 0, 8, 8, 40, 48, 80, 88, 152, 160, 232, 264, 304, 344, 448, 480, 608, 648, 720, 784, 944, 968, 1104, 1176, 1304, 1376, 1576, 1616, 1840, 1944, 2080, 2184, 2352, 2424, 2688, 2816, 2984, 3072, 3368, 3440, 3760, 3896, 4064, 4224, 4576, 4664, 4984, 5120
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OFFSET

0,6


COMMENTS

a(n) mod 8 = 0.


LINKS



MAPLE

df:= proc(n) local count, c, d, q, av, bc, a, b;
count:= 0:
for d from 1 to n1 do
av:= {$1..n1} minus {d};
for q in [1, 1] do
bc:= n*d+q;
for b in numtheory:divisors(bc) intersect av do
c:= bc/b;
if c < b and member(c, av) then count:=count+8 fi;
od od od;
count
end proc:
ListTools:PartialSums(map(df, [$0..100])); # Robert Israel, Nov 29 2016


MATHEMATICA

df[n_] := Module[{count = 0, c, d, q, av, bc, a, b}, Do[av = Range[n  1] ~Complement~ {d}; Do[bc = n d + q; Do[c = bc/b; If[c < b && MemberQ[av, c], count += 8], {b, Divisors[bc] ~Intersection~ av}], {q, {1 , 1}}], {d, 1, n  1}]; count];


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 abs(a*db*c)==1:
s+=1
return s
for i in range(0, 242):


CROSSREFS

Cf. A210000 (where the matrix entries can be repeated).


KEYWORD

nonn


AUTHOR



STATUS

approved



