%I
%S 1,1,1,1,2,1,3,8,4,8,1,5,18,20,48,16,32,1,7,32,56,160,112,
%T 256,64,128,1,9,50,120,400,432,1120,576,1280,256,512,1,11,72,
%U 220,840,1232,3584,2816,6912,2816,6144,1024,2048,1,13,98,364,1568,2912,9408,9984,26880,16640,39424,13312,28672
%N A triangular sequence of coefficients of even plus odd Chebyshev polynomials, A053120: q(x,n)=T(x,2*n1]+T(x,2*n).
%C The row sums are all 2 and double integrations are all orthogonal except for the zero to one level.
%C This arose from an idea of Chladni Chebyshev's:
%C q(Exp[i*t],n)=T(Cos[2*Pi*t),2*n1)+T(Sin(2*Pi*t),2*n)
%C which are strange looping spirals.
%F q(x,n)=T(x,2*n1]+T(x,2*n).
%e {1, 1},
%e {1, 1, 2},
%e {1, 3, 8, 4, 8},
%e {1, 5,18, 20, 48, 16, 32},
%e {1, 7, 32, 56, 160, 112, 256, 64, 128},
%e {1, 9, 50, 120, 400, 432, 1120, 576, 1280, 256, 512},
%e {1, 11, 72, 220, 840, 1232, 3584, 2816, 6912, 2816, 6144, 1024, 2048},
%e {1, 13, 98, 364, 1568, 2912, 9408, 9984, 26880, 16640, 39424, 13312, 28672, 4096, 8192},
%e {1, 15, 128, 560, 2688, 6048, 21504, 28800, 84480, 70400, 180224, 92160, 212992, 61440, 131072, 16384, 32768},
%e {1, 17, 162, 816, 4320, 11424, 44352, 71808, 228096, 239360, 658944, 452608, 1118208, 487424, 1105920, 278528, 589824, 65536, 131072},
%e {1, 19, 200, 1140, 6600, 20064, 84480, 160512, 549120, 695552, 2050048, 1770496, 4659200, 2723840, 6553600, 2490368, 5570560, 1245184, 2621440, 262144, 524288}
%t Q[x_, n_] := ChebyshevT[2*n  1, x] + ChebyshevT[2*n, x]; Table[ExpandAll[Q[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a0]
%Y Cf. A053120.
%K uned,tabl,sign
%O 1,5
%A _Roger L. Bagula_, Apr 20 2008
