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%I #5 Dec 18 2015 18:17:13
%S 1,0,2,-3,0,4,-12,20,0,-6,24,-84,73,0,-12,48,-256,408,-216,0,18,-48,
%T 480,-1328,1464,-603,0,36,0,704,-3312,5760,-4500,1404,0,-54,-192,0,
%U 4720,-15264,20520,-13212,3537,0,-108,-768,3584,0,-26880,62496,-64512,33264,-7344,0,162,1536,-12288,29440,0,-116256
%N Sign weighted matrices n X n:example {{2 w[2], w[0], w[1]}, {3 w[0], 2 w[1], w[2]}, {3 w[1], 3 w[2], 2 w[0]}} are made into monomials using w[n]=1 if n<>0, x if n==0. The coefficients of the monomials form a triangular sequence.
%C Row sums:
%C {1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1}.
%F Matrix: M(d)=(2 + Sign[n - m])*w[Mod[n + m, d]; If[n == 0, w[n] = x, w[n] = 1]; out_n,m=Coefficients[Det(M(d)))
%e {1},
%e {0, 2},
%e {-3, 0, 4},
%e {-12, 20, 0, -6},
%e {24, -84, 73, 0, -12},
%e {48, -256,408, -216, 0, 18},
%e {-48, 480, -1328, 1464, -603, 0, 36},
%e {0, 704, -3312, 5760, -4500,1404, 0, -54},
%e {-192, 0, 4720, -15264, 20520, -13212, 3537, 0, -108},
%e {-768, 3584, 0, -26880, 62496, -64512, 33264, -7344, 0, 162},
%e {1536, -12288, 29440, 0, -116256, 221760, -195552, 88560, -17523, 0, 324}
%t M[d_] := Table[(2 + Sign[n - m])*w[Mod[n + m, d]], {n, 1, d}, {m, 1, d}]; a = Table[M[d], {d, 1, 10}]; Table[If[n == 0, w[n] = x, w[n] = 1], {n, 0, 10}]; Table[Det[a[[d]]], {d, 1, 10}]; a0 = Join[{{1}}, Table[CoefficientList[Det[a[[d]]], x], {d, 1, 10}]]; Flatten[a0] Table[Apply[Plus, CoefficientList[Det[a[[d]]], x]], {d, 1, 10}];
%K uned,tabl,sign
%O 1,3
%A _Roger L. Bagula_ and _Gary W. Adamson_, May 26 2008
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