A280059 - OEIS

%I #11 Oct 18 2022 15:31:04

%S 1,45,225,637,1377,2541,4225,6525,9537,13357,18081,23805,30625,38637,

%T 47937,58621,70785,84525,99937,117117,136161,157165,180225,205437,

%U 232897,262701,294945,329725,367137,407277,450241,496125

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

%H Indranil Ghosh, <a href="/A280059/b280059.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

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

%F From _G. C. Greubel_, Dec 25 2016: (Start)

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

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

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

%t 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 *)

%o def t(n):

%o     s=0

%o     for a in range(-n,n+1):

%o         for b in range(-n,n+1):

%o             for c in range(-n,n+1):

%o                 for d in range(-n,n+1):

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

%o                         s+=1

%o     return s

%o for i in range(0,1001):

%o     print str(i)+" "+str(t(i))

%o (PARI) for(n=0, 50, print1(16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, ", ")) \\ _G. C. Greubel_, Dec 25 2016

%Y Cf. A210000.

%K nonn,easy

%O 0,2

%A _Indranil Ghosh_, Dec 25 2016