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

0,7

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

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 *)

Prog

(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)))
(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
(C) See Greathouse link.

Crossrefs

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

Sequence in context: A248764 A238409 A040241 * A022350 A226068 A230977

Adjacent sequences: A278345 A278346 A278347 * A278349 A278350 A278351

Keyword

nonn

Author

Indranil Ghosh, Nov 18 2016

Status

approved