Search: id:A123148
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%I A123148
%S A123148 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,
%T A123148 40,20,12,2,1,16,64,80,80,60,24,14,2,1,32,80,160,160,120,84,28,16,2,1,
%U A123148 32,160,240,320,280,168,112,32,18,2,1
%V A123148 -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,
%W A123148 -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,
%X A123148 -32,160,-240,320,-280,168,-112,32,-18,2,-1
%N A123148 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).
%C A123148 Row sums yield -1,-1,-1,... . Alternating row sums yield the Jacobsthal 
               sequence (A001045) with changed signs.
%e A123148 -1
%e A123148 -2+x
%e A123148 -2+2*x-x^2
%e A123148 -4+4*x-2*x^2+x^3
%e A123148 -4+8*x-6*x^2+2*x^3-x^4
%p A123148 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
%t A123148 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]
%Y A123148 Sequence in context: A035369 A129719 A062602 this_sequence A166548 A134997 
               A104605
%Y A123148 Adjacent sequences: A123145 A123146 A123147 this_sequence A123149 A123150 
               A123151
%K A123148 sign,tabl
%O A123148 0,2
%A A123148 Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 01 2006
%E A123148 Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2006

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