A280059 Number of 2 X 2 matrices having all elements in {-n,..,0,..,n} with determinant = permanent.

1, 45, 225, 637, 1377, 2541, 4225, 6525, 9537, 13357, 18081, 23805, 30625, 38637, 47937, 58621, 70785, 84525, 99937, 117117, 136161, 157165, 180225, 205437, 232897, 262701, 294945, 329725, 367137, 407277, 450241, 496125

Offset

0,2

Links

Indranil Ghosh, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3 for n>0.

From G. C. Greubel, Dec 25 2016: (Start)

G.f.: (1 + 41*x + 51*x^2 + 3*x^3)/(1 - x)^4.

E.g.f.: (1 + 44*x + 68*x^2 + 16*x^3)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Mathematica

Table[16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 45, 225, 637}, 50] (* G. C. Greubel, Dec 25 2016 *)

Prog

def t(n):
    s=0
    for a in range(-n, n+1):
        for b in range(-n, n+1):
            for c in range(-n, n+1):
                for d in range(-n, n+1):
                    if (a*d-b*c)==(a*d+b*c):
                        s+=1
    return s
for i in range(0, 1001):
    print str(i)+" "+str(t(i))
(PARI) for(n=0, 50, print1(16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, ", ")) \\ G. C. Greubel, Dec 25 2016

Crossrefs

Cf. A210000.

Sequence in context: A203835 A087442 A334035 * A251451 A251444 A169717

Adjacent sequences: A280056 A280057 A280058 * A280060 A280061 A280062

Keyword

nonn,easy

Author

Indranil Ghosh, Dec 25 2016

Status

approved