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%I #20 Sep 04 2017 05:24:54
%S 1,0,1,1,1,1,3,1,3,3,4,3,7,4,7,7,9,7,13,9,14,13,17,14,22,17,24,22,28,
%T 24,35,28,38,35,43,38,52,43,56,52,63,56,74,63,79,74,88,79,101,88,108,
%U 101,119,108,134,119,143,134,156,143,174,156,185,174,200,185,221,200
%N Expansion of 1/((1-x^2)(1-x^3)(1-x^6)(1-x^10)).
%C A two-way infinite sequences which is palindromic (up to sign). - _Michael Somos_, Mar 21 2003
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 0, -1, 1, 0, -1, -1, 1, 1, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1).
%F G.f.: 1/((1-x^2)(1-x^3)(1-x^6)(1-x^10)).
%F a(n) = A051263(floor(n/2) - n mod 2) = A051263(A028242(n-2)).
%F a(-21 - n) = -a(n).
%F a(n) = a(n-2) + a(n-3) - a(n-5) + a(n-6) - a(n-8) - a(n-9) + a(n-10) + a(n-11) - a(n-12) - a(n-13) + a(n-15) - a(n-16) + a(n-18) + a(n-19) - a(n-21).
%p M := Matrix(21, (i,j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 6, 10, 11, 15, 18, 19])) then 1 elif j=1 and member(i, [5, 8, 9, 12, 13, 16, 21]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..67); # _Alois P. Heinz_, Jul 25 2008
%t CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^6)(1-x^10)),{x,0,80}],x] (* or *) LinearRecurrence[{0,1,1,0,-1,1,0,-1,-1,1,1,-1,-1,0,1,-1,0,1,1,0,-1},{1,0,1,1,1,1,3,1,3,3,4,3,7,4,7,7,9,7,13,9,14},80] (* _Harvey P. Dale_, Aug 07 2015 *)
%o (PARI) a(n)=if(n<-20,-a(-21-n),if(n<0,0,polcoeff(1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^10))+x*O(x^n),n)))
%Y Cf. A028242, A051263.
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_
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