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A164359 Expansion of (1 - x^2)^3 / ((1 - x)^3 * (1 - x^3)) in powers of x.

%I A164359 #17 Aug 16 2021 13:40:41
%S A164359 1,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,
%T A164359 3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,
%U A164359 3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3,2,3,3
%N A164359 Expansion of (1 - x^2)^3 / ((1 - x)^3 * (1 - x^3)) in powers of x.
%H A164359 G. C. Greubel, <a href="/A164359/b164359.txt">Table of n, a(n) for n = 0..1000</a>
%H A164359 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A164359 Euler transform of length 3 sequence [ 3, -3, 1].
%F A164359 Moebius transform is length 3 sequence [ 3, 0, -1].
%F A164359 a(-n) = a(n) for all n in Z. a(n+3) = a(n) unless n=0 or n=-3. a(3*n) = 2 unless n=0. a(3*n + 1) = a(3*n + 2) = 3.
%F A164359 G.f.: -1 + (1/3) * ( 8 / (1 - x) - (2 + x) / (1 + x + x^2) ).
%F A164359 a(n) = A244893(n) if n>1. - _Michael Somos_, Apr 17 2015
%e A164359 G.f. = 1 + 3*x + 3*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 2*x^6 + 3*x^7 + 3*x^8 + 2*x^9 + ...
%t A164359 a[ n_] := -Boole[n == 0] + 2 + KroneckerSymbol[ 9, n]; (* _Michael Somos_, Apr 17 2015 *)
%t A164359 CoefficientList[Series[(1-x^2)^3/((1-x)^3*(1-x^3)),{x,0,120}],x] (* or *) LinearRecurrence[{0,0,1},{1,3,3,2},120] (* or *) PadRight[{1},120,{2,3,3}] (* _Harvey P. Dale_, Aug 16 2021 *)
%o A164359 (PARI) {a(n) = -(n==0) + 2 + kronecker(9, n)};
%Y A164359 Cf. A244893.
%K A164359 nonn,easy
%O A164359 0,2
%A A164359 _Michael Somos_, Aug 13 2009