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Search: id:A124033
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| A124033 |
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Triangle read by rows: T(n,k) is the coefficient of x^k in the determinant of the n X n tridiagonal matrix with 1's on the main diagonal and x^(1/2) on the sub- and superdiagonal (n>=1, 0<=k<=floor(n/2)). |
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+0
1
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| 1, 1, -1, 1, -2, 1, -3, 1, 1, -4, 3, 1, -5, 6, -1, 1, -6, 10, -4, 1, -7, 15, -10, 1, 1, -8, 21, -20, 5, 1, -9, 28, -35, 15, -1, 1, -10, 36, -56, 35, -6, 1, -11, 45, -84, 70, -21, 1, 1, -12, 55, -120, 126, -56, 7, 1, -13, 66, -165, 210, -126, 28, -1, 1, -14, 78, -220, 330, -252, 84, -8, 1, -15, 91, -286, 495, -462, 210, -36, 1
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row n contains 1+floor(n/2) terms. With x on the main diagonal and 1's on the sub- and superdiagonal, one obtains A049310.
Conjecture: this is A115139 with its first row deleted. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2008
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EXAMPLE
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Setting y=sqrt(x), we have det(matrix({1,y,0,0},{y,1,y,0},{0,y,1,y},{0,0,y,1}))=1-3x+x^2, leading to row 4 of the triangle.
Triangle starts:
1;
1,-1;
1,-2;
1,-3,1;
1,-4,3;
1,-5,6,-1;
1,-6,10,-4;
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MAPLE
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with(linalg): m:=proc(i, j) if i=j then 1 elif abs(i-j)=1 then sqrt(x) else 0 fi end: T:=(n, k)->coeff(det(matrix(n, n, m)), x, k): for n from 1 to 16 do seq(T(n, k), k=0..floor(n/2)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A049310.
Sequence in context: A122610 A011973 A115139 this_sequence A112543 A099478 A133913
Adjacent sequences: A124030 A124031 A124032 this_sequence A124034 A124035 A124036
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KEYWORD
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sign,tabf
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Nov 01 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2006
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