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Search: id:A103283
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| A103283 |
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Triangle read by rows: T(n,k) is the coefficient of x^k (0<=k<=n)in the monic characteristic polynomial of the n by n matrix with 2's on the diagonal and 1's elsewhere (n>=1). Row 0 consists of the single term 1. |
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+0
3
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| 1, -2, 1, 3, -4, 1, -4, 9, -6, 1, 5, -16, 18, -8, 1, -6, 25, -40, 30, -10, 1, 7, -36, 75, -80, 45, -12, 1, -8, 49, -126, 175, -140, 63, -14, 1, 9, -64, 196, -336, 350, -224, 84, -16, 1, -10, 81, -288, 588, -756, 630, -336, 108, -18, 1, 11, -100, 405, -960, 1470, -1512, 1050, -480, 135, -20, 1, -12, 121, -550, 1485, -2640
(list; table; graph; listen)
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OFFSET
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0,2
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EXAMPLE
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The monic characteristic polynomial of the matrix [2 1 1 / 1 2 1 / 1 1 2] is x^3 - 6x^2 + 9x - 4; so T(3,0)=-4, T(3,1)=9, T(3,2)=-6, T(3,3)=1.
Triangle begins:
1;
-2,1;
3,-4,1;
-4,9,-6,1;
5,-16,18,-8,1;
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MAPLE
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with(linalg): a:=proc(i, j) if i=j then 2 else 1 fi end: 1; for n from 1 to 11 do seq(coeff(expand(x*charpoly(matrix(n, n, a), x)), x^k), k=1..n+1) od; # yields the sequence in triangular form
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CROSSREFS
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Row sums yield the sequence 1,-1,0,0,0,... . Row sums of the unsigned triangle yield A001792. See A093375 for a signed version. A103406 is a mirror image.
Cf. A001792.
Sequence in context: A072506 A133807 A093375 this_sequence A104698 A067066 A125103
Adjacent sequences: A103280 A103281 A103282 this_sequence A103284 A103285 A103286
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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), Feb 04 2005
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EXTENSIONS
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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 19 2005
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