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Search: id:A103406
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| A103406 |
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Triangle read by rows: n-th row = unsigned coefficients of the characteristic polynomials of an n X n matrix with 2's on the diagonal and 1's elsewhere. |
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+0
7
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| 1, 1, 2, 1, 4, 3, 1, 6, 9, 4, 1, 8, 18, 16, 5, 1, 10, 30, 40, 25, 6, 1, 12, 45, 80, 75, 36, 7, 1, 14, 63, 140, 175, 126, 49, 8, 1, 16, 84, 224, 350, 336, 196, 64, 9, 1, 18, 108, 336, 630, 756, 588, 288, 81, 10, 1, 20, 135, 480, 1050, 1512, 1470, 960, 405, 100, 11, 1, 22, 165
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The first few characteristic polynomials are:
1
x - 2
x^2 - 4x + 3
x^3 - 6x^2 + 9x - 4
x^4 - 8x^3 + 18x^2 - 16x + 5
This triangle * [1/1, 1/2, 1/3,...] = (1, 2, 4, 8, 16, 32,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 15 2007
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FORMULA
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Binomial transform of A127648. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 15 2007
Equals A128064 * A007318 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 03 2008
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EXAMPLE
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Characteristic polynomial of 3 X 3 matrix [2 1 1 / 1 2 1 / 1 1 2] = x^3 - 6x^2 + 9x - 4.
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MAPLE
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with(linalg): printf(`%d, `, 1): for n from 1 to 15 do mymat:=array(1..n, 1..n): for i from 1 to n do for j from 1 to n do if i=j then mymat[i, j]:=2 else mymat[i, j]:=1 fi: od: od: temp:=charpoly(mymat, x): for j from n to 0 by -1 do printf(`%d, `, abs(coeff(temp, x, j))) od: od: (Sellers)
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CROSSREFS
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Row sums = A001792: 1, 3, 8, 20, 48, 112...
See A103283 for the mirror image. Cf. A093375.
Cf. A127648.
Cf. A128064.
Sequence in context: A134543 A093010 A093966 this_sequence A093190 A132191 A094437
Adjacent sequences: A103403 A103404 A103405 this_sequence A103407 A103408 A103409
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 04 2005
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 22 2005
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