The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 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 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 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 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 16:04 EST 2023. Contains 367540 sequences. (Running on oeis4.)