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Search: id:A123148
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| A123148 |
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Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial p[n,x] defined by p[0,x]=-1, p[1,x]=x-2, p[n,x]=-xp[n-1,x]+2p[n-2,x] for n>=3 (0<=k<=n). |
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+0
1
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| -1, -2, 1, -2, 2, -1, -4, 4, -2, 1, -4, 8, -6, 2, -1, -8, 12, -12, 8, -2, 1, -8, 24, -24, 16, -10, 2, -1, -16, 32, -48, 40, -20, 12, -2, 1, -16, 64, -80, 80, -60, 24, -14, 2, -1, -32, 80, -160, 160, -120, 84, -28, 16, -2, 1, -32, 160, -240, 320, -280, 168, -112, 32, -18, 2, -1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums yield -1,-1,-1,... . Alternating row sums yield the Jacobsthal sequence (A001045) with changed signs.
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EXAMPLE
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-1
-2+x
-2+2*x-x^2
-4+4*x-2*x^2+x^3
-4+8*x-6*x^2+2*x^3-x^4
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MAPLE
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p[0]:=-1: p[1]:=x-2: for n from 2 to 10 do p[n]:=sort(expand(-x*p[n-1]+2*p[n-2])) od: for n from 0 to 10 do seq(coeff(p[n], x, k), k=0..n) od; # yields sequence in triangular form
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MATHEMATICA
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a = -1; b = 2; p[0, x] = -1; p[1, x] = x - 2; p[k_, x_] := p[k, x] = a*x*p[k - 1, x] + b*p[k - 2, x] w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
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CROSSREFS
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Adjacent sequences: A123145 A123146 A123147 this_sequence A123149 A123150 A123151
Sequence in context: A035369 A129719 A062602 this_sequence A166548 A134997 A104605
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KEYWORD
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sign,tabl
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 01 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2006
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