1,2

This kind of sequence was suggested by a fourth power set of polynomials in one of Karem Boubaker's papers.

Row sum here is repeating in magnitude:

Table[Apply[Plus, CoefficientList[B[x, n] /. x -> Sqrt[y], y]], {n, 0, 20, 2}];

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

it appear that the first author here has used the term 'Boubaker Polynomial'

and not Karem Boubaker himself?

Hedi Labiadh, Karem Boubaker, "A Sturm-Loiville shaped characteristic differential equation as a guide to establish a quasi-polynomial expression to the Boubaker polynomials" Differential Equations and Control Processes, #2,2007, ISSN 1817-2172

B(x, n) = x*B(x, n - 1) - B(x, n - 2); p(y,n)=B[Sqrt[y],2*n)

{1},

{2, 1},

{-2, 0, 1},

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

{-2, 8, 0, -4, 1},

{2, -15, 10, 7, -6, 1},

{-2, 24, -35, 0, 18, -8, 1},

{2, -35, 84, -42, -30, 33, -10, 1},

{-2, 48, -168, 168,0, -88, 52, -12, 1},

{2, -63, 300, -462, 198, 143, -182, 75, -14,1},

{-2, 80, -495, 1056, -858, 0, 455, -320, 102, -16, 1}

Clear[B, a] B[x, 0] = 1; B[x, 1] = x; B[x, 2] = 2 + x^2; B[x, 4] = -2 + x^4; B[ x, 3] = x + x^3; B[x_, n_] := B[x, n] = x*B[x, n - 1] - B[x, n - 2]; a = Table[CoefficientList[B[x, n] /. x -> Sqrt[y], y], {n, 0, 20, 2}]; Flatten[a]

Cf. A135929, A138034.

Sequence in context: A114002 A114004 A049986 this_sequence A063574 A028933 A127170

Adjacent sequences: A137286 A137287 A137288 this_sequence A137290 A137291 A137292

nonn,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 14 2008