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A109588 n followed by n^2 followed by n^3.

%I A109588 #38 Jan 10 2020 20:01:31
%S A109588 1,1,1,2,4,8,3,9,27,4,16,64,5,25,125,6,36,216,7,49,343,8,64,512,9,81,
%T A109588 729,10,100,1000,11,121,1331,12,144,1728,13,169,2197,14,196,2744,15,
%U A109588 225,3375,16,256,4096,17,289,4913,18,324,5832,19,361,6859,20,400,8000
%N A109588 n followed by n^2 followed by n^3.
%H A109588 Muniru A Asiru, <a href="/A109588/b109588.txt">Table of n, a(n) for n = 1..5000</a>
%H A109588 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).
%F A109588 From _R. J. Mathar_, Mar 30 2009: (Start)
%F A109588 a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) - a(n-12).
%F A109588 a(3*k+1) = k+1, a(3*k+2) = A000290(k+1), a(3*k+3) = A000578(k+1).
%F A109588 G.f.: x*(1 + x + x^2 - 2*x^3 + 4*x^5 + x^6 - x^7 + x^8)/((1 - x)^4*(1 + x + x^2)^4). (End)
%F A109588 a(n) = floor((n + 2)/3)*((1 - (-1)^(2^(n + 2 - 3*floor((n + 2)/3))))/2 + floor((n + 2)/3)*(1 - (-1)^(2^(n + 1 - 3*floor((n + 1)/3))))/2 + (floor((n + 2)/3))^2*(1 - (-1)^(2^(n - 3*floor(n/3))))/2). - _Luce ETIENNE_, Dec 16 2014
%F A109588 E.g.f.: ((2*x^3 + 3*x^2 + 8*x - 21)*exp(-x/2)*cos(sqrt(3)*x/2) + (3*x^2 + 8*x + 15)*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2) + (x^3 + 6*x^2 + 19*x + 21)*exp(x))/81. - _Robert Israel_, Dec 17 2014
%p A109588 seq(seq(n^k, k=1..3), n=1..20); # _Zerinvary Lajos_, Jun 29 2007
%t A109588 CoefficientList[Series[(1 + x + x^2 - 2*x^3 + 4*x^5 + x^6 - x^7 + x^8)/((1 - x)^4*(1 + x + x^2)^4), {x, 0, 20}], x] (* _Stefano Spezia_, Sep 12 2018 *)
%t A109588 Table[{n,n^2,n^3},{n,20}]//Flatten (* or *) LinearRecurrence[{0,0,4,0,0,-6,0,0,4,0,0,-1},{1,1,1,2,4,8,3,9,27,4,16,64},60] (* _Harvey P. Dale_, Jan 10 2020 *)
%o A109588 (GAP) Flat(List([1..20],n->[n,n^2,n^3])); # _Muniru A Asiru_, Sep 12 2018
%Y A109588 Cf. A000463.
%K A109588 nonn,easy
%O A109588 1,4
%A A109588 _Mohammad K. Azarian_, Aug 30 2005