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A280914 Number of 2 X 2 matrices with all terms in {-n,...,0,...,n} and (sum of terms) = permanent.

%I A280914 #40 Jun 10 2025 01:15:16
%S A280914 1,21,52,172,268,428,588,812,1004,1324,1580,1900,2252,2668,2988,3532,
%T A280914 3916,4460,5004,5548,6028,6764,7308,8044,8716,9548,10156,11116,11852,
%U A280914 12620,13548,14444,15244,16524,17228,18380,19340,20588,21548
%N A280914 Number of 2 X 2 matrices with all terms in {-n,...,0,...,n} and (sum of terms) = permanent.
%C A280914 a(n) mod 4 = 0 for n > 1.
%H A280914 David Radcliffe, <a href="/A280914/b280914.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..168 from Indranil Ghosh).
%e A280914 For n = 4, a few of the possible matrices are [-4,-3,-2,3], [-4,-3,3,-1], [-4,-2,-3,3], [-4,-2,2,0], [-3,4,-1,-1], [-3,4,3,2], [-2,-4,0,2], [-2,-4,3,-3], [-1,4,1,0], [-1,4,3,3], [0,-4,0,4], [0,-4,1,-1], [0,-3,0,3], [1,2,3,0], [1,2,3,1], [1,2,3,2], [1,2,3,3], [1,2,3,4], [1,3,2,-4], [1,3,2,-3], [2,-1,0,1],... There are 268 possibilities.
%e A280914 Here each of the matrices M is defined as M = [a,b;c,d] where a = M[1][1], b = M[1][2], c = M[2][1] and d = M[2][2]. So, a(4) = 268.
%o A280914 (Python)
%o A280914 def t(n):
%o A280914     s=0
%o A280914     for a in range(-n,n+1):
%o A280914         for b in range(-n,n+1):
%o A280914             for c in range(-n,n+1):
%o A280914                 for d in range(-n,n+1):
%o A280914                     if (a+b+c+d)==(a*d+b*c):
%o A280914                         s+=1
%o A280914     return s
%o A280914 for i in range(0,169):
%o A280914     print(f"{i} {t(i)}")
%Y A280914 Cf. A280588, A280934, A281194.
%K A280914 nonn
%O A280914 0,2
%A A280914 _Indranil Ghosh_, Jan 18 2017