login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280058 Number of 2 X 2 matrices with entries in {0,1,...,n} with determinant = permanent with no entries repeated. 1
0, 0, 0, 12, 48, 120, 240, 420, 672, 1008, 1440, 1980, 2640, 3432, 4368, 5460, 6720, 8160, 9792, 11628, 13680, 15960, 18480, 21252, 24288, 27600, 31200, 35100, 39312, 43848, 48720, 53940, 59520, 65472, 71808, 78540, 85680, 93240, 101232, 109668, 118560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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) = 2*((n+1)^3 - 6*(n+1)^2 + 11*(n+1) - 6), for n>0.

a(n) == 12 (mod 12).

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

G.f.: (12*x^3)/(1 - x)^4.

E.g.f.: 2*x^3*exp(x).

a(n) = 2*n*(n-1)*(n-2).

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

a(n) = 12 * A000292(n-2) for n>1. - Alois P. Heinz, Jan 30 2017

MATHEMATICA

Table[2*n*(n-1)*(n-2), {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 0, 0, 12}, 50] (* G. C. Greubel, Dec 25 2016 *)

PROG

(Python)

def t(n):

    s=0

    for a in range(0, n+1):

        for b in range(0, n+1):

            if a!=b:

                for c in range(0, n+1):

                    if a!=c and b!=c:

                        for d in range(0, n+1):

                            if d!=a and d!=b and d!=c:

                                if (a*d-b*c)==(a*d+b*c):

                                    s+=1

    return s

for i in range(0, 201):

    print str(i)+" "+str(t(i))

(PARI) for(n=0, 50, print1(2*n*(n-1)*(n-2), ", ")) \\ G. C. Greubel, Dec 25 2016

(PARI) a(n)=12*binomial(n, 3) \\ Charles R Greathouse IV, Dec 25 2016

CROSSREFS

Cf. A000292, A015237 (where the entries can be repeated).

Sequence in context: A256695 A135453 A165280 * A173548 A006564 A239352

Adjacent sequences:  A280055 A280056 A280057 * A280059 A280060 A280061

KEYWORD

nonn,easy

AUTHOR

Indranil Ghosh, Dec 25 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 03:42 EST 2019. Contains 329388 sequences. (Running on oeis4.)