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Search: id:A140059
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| A140059 |
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Triangle read by rows: characteristic polynomials of Z/NZ addition tables considered as matrices. |
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+0
1
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| 1, 1, -1, 1, -3, -3, 9, 1, -4, -20, 32, 96, 1, -10, -25, 250, 125, -1250, 1, -12, -93, 576, 2592, -5184, -19440, 1, -21, -98, 2058, 2401, 50421, 16807, 352947, 1, -24, -272, 3840, 24064, -147456, -753664, 1572864, 7340032
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Determinant of n-th order matrix (irrespective of sign) = rightmost term of n-th order polynomial.
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FORMULA
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n-th row of the triangle is the characteristic polynomial of n-th order (n=N), Z/NZ addition table considered as a matrix.
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EXAMPLE
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Addition table Z/3Z = [0,1,2; 1,2,0; 2,0,1]. Considered as a matrix, the charpoly = x^3 - 3x^2 - 3x + 9.
First few charpolys are:
x;
x^2 - 1;
x^3 - 3x^2 - 3x + 9;
x^4 - 4x^3 - 20x^2 + 32x + 96;
x^5 - 10x^4 - 25x^3 + 250x^2 + 125x - 1250;
x^6 - 12x^5 - 93x^4 + 576x^3 + 2592x^2 - 5194x - 19440;
x^7 - 21x^6 - 98x^5 + 2058x^3 - 50421x^2 - 16807x + 352947;
x^8 - 24x^7 - 272x^6 + 3840x^5 + 24064x^4 - 147456x^3 - 753664x^2 + 1572864x + 7340032;
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CROSSREFS
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Cf. A007070, A140044, A140045, A095897.
Sequence in context: A119006 A109695 A010610 this_sequence A070517 A028232 A060310
Adjacent sequences: A140056 A140057 A140058 this_sequence A140060 A140061 A140062
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KEYWORD
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sign,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), May 03 2008
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