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A138034 Expansion of (1+3*x^2)/(1-x+x^2). 11

%I

%S 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,

%T -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 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,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3

%N Expansion of (1+3*x^2)/(1-x+x^2).

%C Essentially a duplicate of A119910: 1, followed by A119910. - _Joerg Arndt_, Nov 14 2014

%H Karem Boubaker and Lin Zhang, <a href="http://arxiv.org/abs/1203.2082">Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis</a>, arXiv preprint arXiv:1203.2082, 2012. - From _N. J. A. Sloane_, Sep 15 2012

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1).

%F a(n) = A119910(n), n>=1.

%F G.f.: (1+3*x^2)/(1-x+x^2). a(n)=a(n-1)-a(n-2), n>2.

%F 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_, Mar 18 2008

%t CoefficientList[Series[(1 + 3*x^2)/(1 - x + x^2), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Jan 15 2017 *)

%Y Cf. A135929, A135936, A137276.

%K sign,easy

%O 0,3

%A Karem Boubaker (mmbb11112000(AT)yahoo.fr), Mar 01 2008; corrected Mar 03 2008

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Last modified September 20 04:13 EDT 2019. Contains 327212 sequences. (Running on oeis4.)