login
The OEIS is supported by the many generous donors 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
COMMENTS
Consider all Pythagorean triples (X,Y,Z=Y+2) ordered by increasing Z; A005843, A005563, A002522 and A007531 give the X, Y, Z and area A values of related triangles; for n >= 2 altitude h(n) = a(n+1)/A002522(n) or h(n)/2 is irreducible fraction in Q\Z. - Ralf Steiner, Mar 29 2020
LINKS
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
a(n+1) = sqrt(A016742(n)*A099761(n-1)) for n>=2. - Ralf Steiner, Mar 29 2020
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), A005843, A005563, A002522, A016742, A099761, A007531.
Sequence in context: A256695 A135453 A165280 * A173548 A006564 A239352
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)