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%I #17 Sep 08 2022 08:45:20
%S 1,1,1,1,4,8,16,2,9,27,81,3,16,64,256,4,25,125,625,5,36,216,1296,6,49,
%T 343,2401,7,64,512,4096,8,81,729,6561,9,100,1000,10000,10,121,1331,
%U 14641,11,144,1728,20736,12,169,2197,28561,13,196,2744,38416,14,225
%N n^2 followed by n^3 followed by n^4 followed by n.
%H Vincenzo Librandi, <a href="/A110652/b110652.txt">Table of n, a(n) for n = 1..4000</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1).
%F a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+35*n+129-(n^3-n^2+3*n-31)*(-1)^n-(n^3-n^2-29*n+1)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+7*n^2+3*n-95)*(-1)^((2*n+7+(-1)^n)/4))/2048. - _Luce ETIENNE_, Aug 17 2016
%F G.f.: x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*x^10+3*x^11+x^12-x^13+x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5). - _Colin Barker_, Aug 18 2016
%t Flatten[Table[{n^2, n^3, n^4, n}, {n, 40}]] (* _Vincenzo Librandi_, Feb 06 2013 *)
%o (Magma) &cat[[n^2, n^3, n^4, n]: n in [1..20]]; // _Vincenzo Librandi_, Feb 06 2013
%o (PARI) Vec(x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*x^10+3*x^11+x^12-x^13+x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5) + O(x^20)) \\ _Colin Barker_, Aug 18 2016
%Y Cf. A000463, A109588, A109594.
%K nonn,easy
%O 1,5
%A _Mohammad K. Azarian_, Sep 14 2005
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