Search: id:A135929
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%I A135929
%S A135929 1,1,0,1,0,2,1,0,1,0,1,0,0,0,2,1,0,1,0,3,0,1,0,2,0,3,0,2,1,0,3,0,
%T A135929 2,0,5,0,1,0,4,0,0,0,8,0,2,1,0,5,0,3,0,10,0,7,0,1,0,6,0,7,0,10,0,
%U A135929 15,0,2,1,0,7,0,12,0,7,0,25,0,9,0,1,0,8,0,18,0,0,0,35,0,24,0,2,1
%V A135929 1,1,0,1,0,2,1,0,1,0,1,0,0,0,-2,1,0,-1,0,-3,0,1,0,-2,0,-3,0,2,1,0,-3,0,
%W A135929 -2,0,5,0,1,0,-4,0,0,0,8,0,-2,1,0,-5,0,3,0,10,0,-7,0,1,0,-6,0,7,0,10,0,
%X A135929 -15,0,2,1,0,-7,0,12,0,7,0,-25,0,9,0,1,0,-8,0,18,0,0,0,-35,0,24,0,-2,1
%N A135929 Triangle read by rows: row n gives coefficients of Boubaker polynomial 
               B_n(x) in order of decreasing exponents.
%C A135929 See A138034 for references.
%C A135929 Comment from Max Alekseyev, Dec 04 2009: The Boubaker polynomials B_n(X) 
               are related to the Lucas polynomials: B_n(X) = U_n(X,1) + 3 * U_{n-2}(X,
               1) for n>=2.
%D A135929 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 
               1972; see Chapter 22.
%F A135929 Boubaker polynomials have generating function (1+3*t^2)/(1-x*t+t^2). 
               They are related to the Chebyshev polynomials S_n(x), which have 
               g.f. 1/(1-x*t+t^2) (see Abramowitz and Stegun).
%e A135929 The Boubaker polynomials B_0(x), B_1(x), B_2(x), ... are:
%e A135929 1
%e A135929 x
%e A135929 x^2+2
%e A135929 x^3+x
%e A135929 x^4-2
%e A135929 x^5-x^3-3*x
%e A135929 x^6-2*x^4-3*x^2+2
%e A135929 x^7-3*x^5-2*x^3+5*x
%e A135929 x^8-4*x^6+8*x^2-2
%e A135929 x^9-5*x^7+3*x^5+10*x^3-7*x
%e A135929 ...
%p A135929 A135929 := proc(n, m) coeftayl( coeftayl( (1+3*t^2)/(1-x*t+t^2), t=0, 
               n), x=0, n-m) ; end proc: seq(seq(A135929(n,m), m=0..n),n=0..14) 
               ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 03 2009]
%Y A135929 Cf. A138034, A135936.
%Y A135929 Sequence in context: A157424 A144961 A144627 this_sequence A080733 A080732 
               A088568
%Y A135929 Adjacent sequences: A135926 A135927 A135928 this_sequence A135930 A135931 
               A135932
%K A135929 sign,tabl,new
%O A135929 0,6
%A A135929 N. J. A. Sloane (njas(AT)research.att.com), Mar 09 2008
%E A135929 Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 03 2009

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