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A204183
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Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= (-1)^(i-1); f(i,j)=0 otherwise; by antidiagonals.
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3
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1, 1, 1, 1, -1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1
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COMMENTS
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A204183 represents the matrix M given by f(i,j) for i>=1 and j>=1. See A204184 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M.
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LINKS
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Table of n, a(n) for n=1..93.
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EXAMPLE
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Northwest corner:
1...1...1...1...1...1
1..-1...0...0...0...0
1...0...1...0...0...0
1...0...0..-1...0...0
1...0...0...0...1...0
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MATHEMATICA
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f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1;
f[i_, i_] := (-1)^(i - 1);
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
{n, 1, 15}, {i, 1, n}]] (* A204183 *)
p[n_] := CharacteristicPolynomial[m[n], x];
c[n_] := CoefficientList[p[n], x]
TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
Table[c[n], {n, 1, 12}]
Flatten[%] (* A204184 *)
TableForm[Table[c[n], {n, 1, 10}]]
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CROSSREFS
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Cf. A204184, A204016, A202453.
Sequence in context: A194679 A187037 A190230 * A204177 A185917 A190207
Adjacent sequences: A204180 A204181 A204182 * A204184 A204185 A204186
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KEYWORD
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sign,tabl
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AUTHOR
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Clark Kimberling, Jan 12 2012
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STATUS
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approved
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