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%I #3 Mar 30 2012 17:34:26
%S 1,0,2,-1,2,-4,0,-4,4,-8,1,-6,16,-16,16,0,6,-16,40,-32,32,-1,12,-44,
%T 88,-128,96,-64,0,-8,40,-128,208,-288,192,-128,1,-20,100,-296,592,
%U -800,832,-512,256,0,10,-80,328,-800,1472,-1792,1792,-1024,512,-1
%N Triangular sequence from coefficients of a switched even -odd polynomial recursion: odd:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); even:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);.
%C A048788 gives the row sums: {1, 2, -3, -8, 11, 30, -41, -112, 153, 418, -571}
%F p(x,-1)=0;p(x,0)=1;p(x,1]=2*x; odd:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); even:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);
%e {1},
%e {0, 2},
%e {-1, 2, -4},
%e {0, -4, 4, -8},
%e {1, -6, 16, -16,16},
%e {0, 6, -16, 40, -32, 32},
%e {-1, 12, -44, 88, -128, 96, -64},
%e {0, -8, 40, -128, 208, -288, 192, -128},
%e {1, -20, 100, -296, 592, -800, 832, -512, 256},
%e {0,10, -80, 328, -800,1472, -1792, 1792, -1024, 512},
%e {-1, 30, -200, 784, -2048, 3872, -5568, 5888, -4864, 2560, -1024}
%t Clear[p, x, a] p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = 2*x; p[x_, n_] := p[x, n] = If[Mod[n, 2] == 1, 2*x*p[x, n - 1] - p[x, n - 2], (1 - 2*x)*p[x, n - 1] - p[x, n - 2]]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]
%Y Cf. A048788.
%K tabl,uned,sign
%O 1,3
%A _Roger L. Bagula_, Apr 14 2008
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