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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n) mod 8 = 0.

LINKS

Robert Israel, Table of n, a(n) for n = 0..1000 (0..241 from Indranil Ghosh)

MAPLE

df:= proc(n) local count, c, d, q, av, bc, a, b;

  count:= 0:

  for d from 1 to n-1 do

      av:= {$1..n-1} 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];

df /@ Range[0, 100] // Accumulate (* Jean-Fran├žois Alcover, Jul 29 2020, after Robert Israel *)

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*d-b*c)==1:

                            s+=1

    return s

for i in range(0, 242):

    print str(i)+" "+str(t(i)) \\ Indranil Ghosh , Nov 29 2016

CROSSREFS

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

Sequence in context: A111218 A188275 A319019 * A240037 A241867 A243124

Adjacent sequences:  A278843 A278844 A278845 * A278847 A278848 A278849

KEYWORD

nonn,changed

AUTHOR

Indranil Ghosh, Nov 29 2016

STATUS

approved

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)