%I A138034
%S A138034 1,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,
%T A138034 3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,
%U A138034 1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3
%V A138034 1,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,
               -3,-2,1,3,2,-1,
%W A138034 -3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,
               2,-1,-3,-2,1,3,2,
%X A138034 -1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,
               1,3,2,-1,-3,-2,1,3
%N A138034 Let B_n(x) denote the n-th Boubaker polynomial (see A135929). Then a(n) 
               = B_n(1).
%C A138034 B_n(-1) gives the same sequence up to signs.
%H A138034 Karem Boubaker, <a href="http://dx.doi.org/10.3923/tasr.2007.540.544">
               On modified Boubaker polynomials: Some differential and analytical 
               Properties of the new polynomials issued from an attempt for solving 
               bi-varied Heat Equation</a>, Trends Applied Sci. Res., vol 2 (5) 
               (2007), 540-544.
%H A138034 K. Boubaker, A. Chaouachi, M. Amlouk, H. Bouzouita, <a href="http://dx.doi.org/
               10.1051/epjap:2007005">Enhancement of pyrolysis spray disposal performance 
               using thermal time-response to precursor uniform deposition</a>, 
               Eur. Phys. J. Appl. Phys., 37 (2007), 105-109.
%H A138034 Hedi Labiadh and Karem Boubaker, <a href="http://www.neva.ru/journal/
               j/EN/numbers/2007.2/article.59.html">A Sturm-Liouville shaped characteristic 
               differential equation as a guide to establish a quasi-polynomial 
               expression to the Boubaker polynomials</a>, Differential Equations 
               and Control Processes, No. 2 (2007).
%F A138034 a(n) = A119910(n), n>0.
%F A138034 G.f.: (1+3*x^2)/(1-x+x^2). a(n)=a(n-1)-a(n-2), n>2.
%F A138034 a(n)=3*[C(2*n,n) mod 2]+(1/6)*{-(n mod 6)+2*[(n+1) mod 6]+3*[(n+2) mod 
               6]+[(n+3) mod 6]-2*[(n+4) mod 6]-3*[(n+5) mod 6]}, with n>=0. - Paolo 
               P. Lava (ppl(AT)spl.at), Mar 18 2008
%Y A138034 Cf. A135929, A135936, A137276.
%K A138034 sign,easy,new
%O A138034 0,3
%A A138034 Karem Boubaker (mmbb11112000(AT)yahoo.fr), Mar 01 2008; corrected Mar 
               03 2008
%E A138034 A-numbers corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 
               08 2009