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Search: id:A140693
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| A140693 |
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Triangle read by rows, characteristic polynomials of crossed Pascal's matrices; (n x n bisymmetric matrices in which both diagonals = (n-1)-th row of Pascal's triangle with the rest zeros). Given: row 0 = x. |
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+0
1
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| 1, 1, -2, 1, -4, 4, 1, -8, 12, 1, -16, 76, -96, 1, -32, 260, -400, 1, -64, 1324, -9600, 14400
(list; table; graph; listen)
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OFFSET
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0,3
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EXAMPLE
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First few rows of the triangle as polynomials are:
x
x^2 - 2x
x^3 - 4x^2 + 4x
x^4 - 8x^3 + 12x^2
x^5 - 16x^4 + 76x^3 - 96x^2
x^6 - 32x^5 + 260x^4 - 400x^3
x^7 - 64x^6 + 1324x^5 - 9600x^4 + 14400x^3
...
The crossed 4x4 Pascal's matrix = [1,0,0,1; 0,3,3,0; 0,3,3,0; 1,0,0,1]; (i.e. a bisymmetric matrix with (1,3,3,1) as both diagonals and the rest zeros). Charpoly = x^4 - 8x^3 + 12x^2
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CROSSREFS
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Cf. A007318.
Adjacent sequences: A140690 A140691 A140692 this_sequence A140694 A140695 A140696
Sequence in context: A101559 A122438 A131250 this_sequence A131249 A048807 A134397
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KEYWORD
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sign,tabl
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), May 23 2008
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