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%I #2 Mar 30 2012 17:34:35
%S 1,1,-1,1,-2,1,1,-11,11,-1,1,-12,22,-12,1,1,-21,106,-106,21,-1,1,-30,
%T 255,-708,255,-30,1,1,-91,1065,-3963,3963,-1065,91,-1,1,-92,1156,
%U -5028,7926,-5028,1156,-92,1,1,-101,1880,-12688,34482,-34482,12688,-1880,101
%N Coefficients of polynomials from matrix characteristic polynomials: m(n,m,d)=If[ m <= n, Mod[Binomial[n, m], 2], 0]; M(n)=m(n,m,d).Transpose[m(n,m,d)].Transpose[m(n,m,d)].m(n,m,d)
%C Row sums are:
%C {1, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0,...}.
%C Absolute value row sums are:
%C {1, 2, 4, 24, 48, 256, 1280, 10240, 20480, 98304, 405504,...}.
%C Matrix example is:
%C M(3)={{3, 2, 2},
%C {2, 3, 2},
%C {6, 6, 5}}.
%C I've only managed to get three levels of these:
%C (1,5,5,1),(1,7,7,1),(1,11,11,1)
%C but they seem stable that you get them with combinations of the binomial
%C matrix, the Transpose[] and Reverse[].
%C Plotting them shows that they aren't Sierpinski-Pascal at modulo two.
%F m(n,m,d)=If[ m <= n, Mod[Binomial[n, m], 2], 0];
%F M(n)=m(n,m,d).Transpose[m(n,m,d)].Transpose[m(n,m,d)].m(n,m,d);
%F Out_(n,m)=coefficients(characteristicpolynomial(M(n),x),x)
%e {1},
%e {1, -1},
%e {1, -2, 1},
%e {1, -11, 11, -1},
%e {1, -12, 22, -12, 1},
%e {1, -21, 106, -106, 21, -1},
%e { 1, -30, 255, -708, 255, -30, 1},
%e {1, -91, 1065, -3963, 3963, -1065, 91, -1},
%e {1, -92, 1156, -5028, 7926, -5028, 1156, -92, 1},
%e {1, -101, 1880, -12688, 34482, -34482, 12688, -1880, 101, -1},
%e {1, -110, 2669, -25128, 98706, -152276, 98706, -25128, 2669, -110, 1}
%t Clear[M, T, d, a, x, a0];
%t T[n_, m_, d_] := If[ m <= n, Mod[Binomial[n, m], 2], 0];
%t M[d_] := Table[T[n, m, d], { n, 1, d}, {m, 1, d}].Transpose[Table[T[ n, m, d], {n, 1, d}, { m, 1, d}]].Transpose[Table[T[n, m, d], {n, 1, d}, {m, 1, d}]].Table[ T[n, m, d], {n, 1, d}, {m, 1, d}];
%t a0 = Table[M[d], {d, 1, 10}];
%t Table[Det[M[d]], {d, 1, 10}];
%t Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];
%t a = Join[{{1}}, Table[CoefficientList[ Expand[CharacteristicPolynomial[M[n], x]], x], {n, 1, 10}]];
%t Flatten[a]
%t Join[{1}, Table[Apply[Plus, CoefficientList[ Expand[CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}]];
%K sign,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Mar 14 2009
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