1,6

Row sums are:

{1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2};

Gram-Schmidt vector analysis indicates this is orthogonal.

Table[Table[Integrate[Sqrt[1/(1 - x<sup class="moz-txt-sup">2</sup>)]*Q[x,n]*Q[x, m], {x, -1, 1}], {n, 0, 10}], {m, 0, 10}];

Double function integration on the Chebyshev weight function gives it is triadiagonal orthogonal( a second kind of semi-orthogonal to alternating orthogonal as found in Boubaker and some differential Chebyshevs).

A053120(x,-1)=0,A053120(x,0)=1;A053120(x,1)=x; p(x,n)=A053120(x,n)+A053120(x,n-1)

{1},

{1, 1},

{-1, 1, 2},

{-1, -3, 2, 4},

{1, -3, -8, 4, 8},

{1, 5, -8, -20, 8, 16},

{-1, 5, 18, -20, -48, 16, 32},

{-1, -7, 18, 56, -48, -112,32, 64},

{1, -7, -32, 56,160, -112, -256, 64, 128},

{1, 9, -32, -120, 160, 432, -256, -576, 128,256},

{-1, 9, 50, -120, -400, 432, 1120, -576, -1280, 256, 512}

Clear[B, x, n] (* A053120*) B[x, -1] = 0; B[x, 0] = 1; B[x, 1] = x; B[x_, n_] := B[x, n] = 2*x*B[x, n - 1] - B[x, n - 2]; Table[ExpandAll[B[x, n] + B[x, n - 1]], {n, 0, 10}]; a0 = Table[CoefficientList[B[x, n] + B[x, n - 1], x], {n, 0, 10}]; Flatten[a0] (* alternative definition*) Q[x, 0] = 1; Q[x, 1] = x + 1; Q[x_, n_] := Q[x, n] = B[x, n] + B[x, n - 1];

Cf. A053120.

Adjacent sequences: A136520 A136521 A136522 this_sequence A136524 A136525 A136526

Sequence in context: A023129 A007337 A056892 this_sequence A003963 A003960 A124223

uned,tabl,sign

Roger L. Bagula, Mar 23 2008