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Search: id:A084575
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| A084575 |
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Number of terms in polynomial expression for determinant of generic circulant matrix of order n. |
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+0
2
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| 1, 2, 4, 10, 26, 68, 246, 810, 2704, 7492, 32066, 86500
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OFFSET
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1,2
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COMMENT
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Define an n X n matrix A[i,j] by A[i,j]=x_(i+j), subscripts on x being interpreted mod n. This is a generic circulant matrix. If we expand det(A) we obtain a polynomial in the x_i. Define a(n) to be the number of terms in this polynomial after like terms have been combined. (Replacing det(A) with per(A), the permanent of A, we get sequence A003239).
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LINKS
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Hugh Thomas, The number of terms in the permanent ...
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FORMULA
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a(n) <= A003239(n), with = if n is a prime power. For other values of n little is known.
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EXAMPLE
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Example : for n=2 the matrix is
x2,x1
x1,x2
and the determinant is (x_2)^2 - (x_1)^2 so a(2) = 2 and likewise for the permanent.
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CROSSREFS
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Cf. A003239.
Sequence in context: A052995 A055819 A113337 this_sequence A081881 A134773 A025565
Adjacent sequences: A084572 A084573 A084574 this_sequence A084576 A084577 A084578
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 13 2003
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