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Search: id:A123967
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| A123967 |
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Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the tridiagonal n X n matrix with main diagonal 5,5,5,... and sub- and superdiagonals 1,1,1,... (0<=k<=n). |
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+0
2
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| 1, -5, 1, 24, -10, 1, -115, 73, -15, 1, 551, -470, 147, -20, 1, -2640, 2828, -1190, 246, -25, 1, 12649, -16310, 8631, -2400, 370, -30, 1, -60605, 91371, -58275, 20385, -4225, 519, -35, 1, 290376, -501150, 374115, -157800, 41140, -6790, 693, -40, 1, -1391275, 2704755, -2313450, 1142730, -359275, 74571
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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T(n,0)=(-1)^n*A004254(n+1).
Riordan array (1/(1+5*x+x^2),x/(1+5*x+x^2)) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 03 2007
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REFERENCES
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Eric Weisstein's World of Mathematics, "Tridiagonal Matrix." http://mathworld.wolfram.com/TridiagonalMatrix.html
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EXAMPLE
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Triangle starts:
1;
-5, 1,
24, -10, 1,
-115, 73,-15, 1,
551, -470, 147, -20, 1,
-2640, 2828, -1190, 246, -25, 1,
12649, -16310, 8631, -2400, 370, -30, 1,
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MAPLE
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with(linalg): m:=proc(i, j) if i=j then 5 elif abs(i-j)=1 then 1 else 0 fi end: T:=(n, k)->coeff(charpoly(matrix(n, n, m), x), x, k): 1; for n from 1 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A123343.
Cf. A004254.
Sequence in context: A167572 A147476 A146675 this_sequence A162259 A077195 A038243
Adjacent sequences: A123964 A123965 A123966 this_sequence A123968 A123969 A123970
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KEYWORD
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tabl,sign
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 28 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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