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A323255
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The permanent of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 2*n - 1, n - 1, ..., 1 and whose first column consists of 2*n - 1, 2*n - 2, ..., n.
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2
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1, 1, 11, 248, 9968, 638772, 60061657, 7798036000, 1336715859150, 292406145227392, 79483340339739367, 26280500564448081664, 10386012861097225139356, 4834639222955142417477888, 2618110215141486526589786501, 1631888040186649673361825042432, 1159983453675106278249250918734938
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OFFSET
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0,3
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COMMENTS
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The trace of the matrix M(n) is A000384(n).
The sum of the first row of the matrix M(n) is A034856(n).
The sum of the first column of the matrix M(n) is A000326(n).
For n > 1, the sum of the superdiagonal of the matrix M(n) is A000290(n-1).
For n > 1, the sum of the subdiagonal of the matrix M(n) is A001105(n-1).
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LINKS
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EXAMPLE
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For n = 1 the matrix M(1) is
1
with permanent a(1) = 1.
For n = 2 the matrix M(2) is
3, 1
2, 3
with permanent a(2) = 11.
For n = 3 the matrix M(3) is
5, 2, 1
4, 5, 2
3, 4, 5
with permanent a(3) = 248.
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MATHEMATICA
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b[i_]:=i; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Join[{b[2*n-1]}, Array[b, n-1, {2*n-2, n }]], Join[{b[2*n-1]}, Array[b, n-1, {n-1, 1}]]]]]; Array[a, 16, 0]
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PROG
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(PARI) tm(n) = {my(m = matrix(n, n, i, j, if (j==1, 2*n-i, n-j+1))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }
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CROSSREFS
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Cf. A323254 (determinant of matrix M(n)).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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