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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-François 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: A341247 A188275 A319019 * A339323 A240037 A241867 Adjacent sequences: A278843 A278844 A278845 * A278847 A278848 A278849 KEYWORD nonn AUTHOR Indranil Ghosh, Nov 29 2016 STATUS approved

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)