%I A137289
%S A137289 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,
%T A137289 42,30,33,10,1,2,48,168,168,0,88,52,12,1,2,63,300,462,198,143,182,75,14,
%U A137289 1,2,80,495,1056,858,0,455,320,102,16,1
%V A137289 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,
%W A137289 -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,
%X A137289 -495,1056,-858,0,455,-320,102,-16,1
%N A137289 Triangle of coefficients of Boubaker polynomials.
%C A137289 This was suggested by a set of polynomials in one of Karem Boubaker's 
               papers.
%C A137289 Row sums repeat in magnitude:
%C A137289 Table[Apply[Plus, CoefficientList[B[x, n] /. x -> Sqrt[y], y]], {n, 0, 
               20, 2}];
%C A137289 {1, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, ...}.
%D A137289 Hedi Labiadh and 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
%F A137289 B(x, n) = x*B(x, n - 1) - B(x, n - 2); p(y,n)=B[Sqrt[y],2*n)
%e A137289 {1},
%e A137289 {2, 1},
%e A137289 {-2, 0, 1},
%e A137289 {2, -3, -2, 1},
%e A137289 {-2, 8, 0, -4, 1},
%e A137289 {2, -15, 10, 7, -6, 1},
%e A137289 {-2, 24, -35, 0, 18, -8, 1},
%e A137289 {2, -35, 84, -42, -30, 33, -10, 1},
%e A137289 {-2, 48, -168, 168,0, -88, 52, -12, 1},
%e A137289 {2, -63, 300, -462, 198, 143, -182, 75, -14,1},
%e A137289 {-2, 80, -495, 1056, -858, 0, 455, -320, 102, -16, 1}
%t A137289 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]
%Y A137289 Cf. A135929, A138034.
%Y A137289 Sequence in context: A114002 A114004 A049986 this_sequence A063574 A144515 
               A028933
%Y A137289 Adjacent sequences: A137286 A137287 A137288 this_sequence A137290 A137291 
               A137292
%K A137289 sign,tabl
%O A137289 1,2
%A A137289 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 14 2008
%E A137289 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 05 2009