A137406 - OEIS

%I #3 Mar 30 2012 17:34:26

%S 1,1,-2,-1,2,-4,-2,6,-8,8,1,-6,16,-16,16,3,-14,36,-56,48,-32,-1,12,

%T -44,88,-128,96,-64,-4,28,-104,232,-352,384,-256,128,1,-20,100,-296,

%U 592,-800,832,-512,256,5,-50,244,-728,1536,-2368,2688,-2304,1280,-512,-1,30,-200,784,-2048,3872,-5568,5888,-4864,2560,-1024

%N Triangular sequence from coefficients of a switched even -odd polynomial recursion: Even:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); Odd:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);.

%C A002530 is the row sums:

%C {1, -1, -3, 4, 11, -15, -41, 56, 153, -209, -571}

%F p(x,-1)=0;p(x,0)=1;p(x,1]=1-28x; Even:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); Odd:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);

%e {1},

%e {1, -2},

%e {-1, 2, -4},

%e {-2, 6, -8, 8},

%e {1, -6, 16, -16, 16},

%e {3, -14, 36, -56, 48, -32},

%e {-1, 12, -44, 88, -128, 96, -64},

%e {-4, 28, -104, 232, -352, 384, -256, 128},

%e {1, -20, 100, -296, 592, -800, 832, -512, 256},

%e {5, -50, 244, -728, 1536, -2368, 2688, -2304, 1280, -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] = 1 - 2*x; p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, 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. A002530.

%K tabl,uned,sign

%O 1,3

%A _Roger L. Bagula_, Apr 14 2008