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

%I A280059 #11 Oct 18 2022 15:31:04
%S A280059 1,45,225,637,1377,2541,4225,6525,9537,13357,18081,23805,30625,38637,
%T A280059 47937,58621,70785,84525,99937,117117,136161,157165,180225,205437,
%U A280059 232897,262701,294945,329725,367137,407277,450241,496125
%N A280059 Number of 2 X 2 matrices having all elements in {-n,..,0,..,n} with determinant = permanent.
%H A280059 Indranil Ghosh, <a href="/A280059/b280059.txt">Table of n, a(n) for n = 0..1000</a>
%H A280059 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A280059 a(n) = 16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3 for n>0.
%F A280059 From _G. C. Greubel_, Dec 25 2016: (Start)
%F A280059 G.f.: (1 + 41*x + 51*x^2 + 3*x^3)/(1 - x)^4.
%F A280059 E.g.f.: (1 + 44*x + 68*x^2 + 16*x^3)*exp(x).
%F A280059 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%t A280059 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 A280059 def t(n):
%o A280059     s=0
%o A280059     for a in range(-n,n+1):
%o A280059         for b in range(-n,n+1):
%o A280059             for c in range(-n,n+1):
%o A280059                 for d in range(-n,n+1):
%o A280059                     if (a*d-b*c)==(a*d+b*c):
%o A280059                         s+=1
%o A280059     return s
%o A280059 for i in range(0,1001):
%o A280059     print str(i)+" "+str(t(i))
%o A280059 (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 A280059 Cf. A210000.
%K A280059 nonn,easy
%O A280059 0,2
%A A280059 _Indranil Ghosh_, Dec 25 2016