A278348 Number of 2 X 2 singular integer matrices with elements from {0,...,n} with no elements repeated.

0, 0, 0, 0, 0, 0, 16, 16, 32, 40, 72, 72, 136, 136, 184, 248, 304, 304, 408, 408, 536, 632, 712, 712, 920, 968, 1064, 1168, 1360, 1360, 1664, 1664, 1848, 2008, 2136, 2328, 2696, 2696, 2840, 3032, 3432, 3432, 3880, 3880, 4200, 4592, 4768, 4768, 5336, 5456, 5824

Offset: 0

Author

Indranil Ghosh, Nov 18 2016

Keywords

• nonn

Comments

If p is prime then a(p) = a(p-1). - Robert G. Wilson v, Nov 20 2016

Links

• Indranil Ghosh, Charles R Greathouse IV and Chai Wah Wu, Table of n, a(n) for n = 0..10000 (first 101 terms from Ghosh, next 1900 terms from Charles R Greathouse IV)
• Charles R Greathouse IV, C program for computing this sequence

Crossrefs

Cf. A059306 (where in the matrices each element can be present multiple times).

Programs

C

See Greathouse link.

Mathematica

f[n_] := f[n] = Block[{a = 1, b, c, s = 0}, While[b = a + 1; a < n + 1, While[c = b + 1; b < n + 1, While[c < n + 1, If[a != b && a != c && a != n && b != c && b != n && c != n && a*n == b*c, s++]; c++]; b++]; a++]; 8 s + f[n - 1]]; f[0] = 0; Array[f, 51] (* or *)
g[n_] := g[n] = Block[{c = 0, k = 1}, While[k < n, c += Count[ Times @@@ Select[ Tuples[ Rest@ Most@ Divisors[k*n], 2], #[[1]] < #[[2]] < n &], k*n]; k++]; c]; 8*Accumulate[ Array[g, 51]] (* much faster but both are recursive *) (* Robert G. Wilson v, Nov 20 2016 *)

PARI

try(a,b,c,n)=my(d=b*c/a); denominator(d)==1 && d<=n && d!=a && d!=b && d!=c
a(n)=2*sum(a=3,n, sum(b=2,a-1, sum(c=1,b-1, try(a,b,c,n) + try(c,a,b,n) + try(b,a,c,n)))) \\ Charles R Greathouse IV, Nov 20 2016

Python

def p(n):
    s=0
    for a in range(n+1):
        for b in range(n+1):
            for c in range(n+1):
                for d in range(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:
                            s+=1
    return s
for i in range(101):
    print(str(i)+" "+str(p(i)))