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Expansion of (x^3-1+sqrt((x^4+x^3+4*x^2+x+1)*(x^2-x+1)))/(2*x^2).
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%I #18 Aug 19 2022 04:40:40

%S 1,0,0,1,0,-2,1,4,-5,-7,18,7,-55,18,146,-155,-322,692,476,-2446,307,

%T 7322,-6276,-18277,33061,33376,-129238,-10899,420594,-276272,-1147125,

%U 1742502,2413761,-7448113,-2292774,25986573,-11940263,-76138258,96229907,178087693,-450647034

%N Expansion of (x^3-1+sqrt((x^4+x^3+4*x^2+x+1)*(x^2-x+1)))/(2*x^2).

%C Coefficients of [sqrt(2)]_q. See link.

%H Sophie Morier-Genoud and Valentin Ovsienko, <a href="https://arxiv.org/abs/2011.10809">Quantum real numbers and q-deformed Conway-Coxeter friezes</a>, arXiv:2011.10809 [math.QA], 2020. See section 3.4.

%F D-finite with recurrence (n+2)*a(n) +4*(n-1)*a(n-2) +(-2*n+5)*a(n-3) +4*(n-4)*a(n-4) +(n-7)*a(n-6)=0. - _R. J. Mathar_, Aug 19 2022

%e G.f. = 1 + x^3 - 2*x^5 + x^6 + 4*x^7 - 5*x^8 - 7*x^9 + 18*x^10 + ...

%o (PARI) my(x='x+O('x^45)); Vec((x^3-1+sqrt((x^4+x^3+4*x^2+x+1)*(x^2-x+1)))/(2*x^2))

%K sign

%O 0,6

%A _Michel Marcus_, Nov 25 2020