A279483 Number of 2 X 2 matrices with entries in {0,1,...,n} and odd determinant with no entry repeated.

0, 0, 0, 8, 24, 144, 240, 672, 960, 2000, 2640, 4680, 5880, 9408, 11424, 17024, 20160, 28512, 33120, 45000, 51480, 67760, 76560, 98208, 109824, 137904, 152880, 188552, 207480, 252000, 275520, 330240, 359040, 425408, 460224, 539784, 581400, 675792, 725040, 836000, 893760, 1023120, 1090320, 1240008

Offset

0,4

Links

Indranil Ghosh, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Formula

From Colin Barker, Dec 13 2016: (Start)

a(n) = (3*n^4 - 8*n^3 - 12*n^2 + 32*n)/8 for n even.

a(n) = (3*n^4 - 4*n^3 - 10*n^2 + 4*n + 7)/8 for n odd.

a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n>8.

G.f.: 8*x^3*(1 + 2*x + 11*x^2 + 4*x^3) / ((1 - x)^5*(1 + x)^4).

(End)

Mathematica

CoefficientList[Series[8 x^3*(1 + 2 x + 11 x^2 + 4 x^3)/((1 - x)^5*(1 + x)^4), {x, 0, 43}], x] (* Michael De Vlieger, Dec 13 2016 *)

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 (a*d-b*c)%2==1:
                            s+=1
    return s
for i in range(0, 201):
    print str(i)+" "+str(t(i))
(PARI) F(n, {r=0})={my(s=vector(2), v); forvec(y=vector(4, j, [0, n]), for(k=23*!!r, 23, v=numtoperm(4, k); s[1+(y[v[1]]*y[v[4]]-y[v[3]]*y[v[2]])%2]++), 2*!r); return(s)} \\ a(n)=F(n, 0)[2];
(PARI) concat(vector(3), Vec(8*x^3*(1 + 2*x + 11*x^2 + 4*x^3) / ((1 - x)^5*(1 + x)^4) + O(x^40))) \\ Colin Barker, Dec 13 2016

Crossrefs

Cf. A210370 (where the entries can be repeated).

Sequence in context: A305224 A182068 A092771 * A098070 A100042 A061027

Adjacent sequences: A279480 A279481 A279482 * A279484 A279485 A279486

Keyword

nonn,easy

Author

Indranil Ghosh, Dec 13 2016

Status

approved