%I #21 Sep 08 2022 08:45:20
%S 1,1,1,1,4,2,8,16,9,3,27,81,16,4,64,256,25,5,125,625,36,6,216,1296,49,
%T 7,343,2401,64,8,512,4096,81,9,729,6561,100,10,1000,10000,121,11,1331,
%U 14641,144,12,1728,20736,169,13,2197,28561,196,14,2744,38416,225,15
%N n^2 followed by n followed by n^3 followed by n^4.
%H Vincenzo Librandi, <a href="/A110622/b110622.txt">Table of n, a(n) for n = 1..8000</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) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20).
%F G.f.: -x*(1 + x + x^2 + x^3 - x^4 - 3*x^5 + 3*x^6 + 11*x^7 - x^8 + 3*x^9 - 3*x^10 + 11*x^11 + x^12 - x^13 - x^14 + x^15) / ( (x-1)^5*(1+x)^5*(x^2+1)^5 ). - _R. J. Mathar_, Dec 20 2010
%F a(n) = (2*n + 3 - (-1)^n + 2*(-1)^((2*n + 5 - (-1)^n)/4))*(n^3 + 4*n^2 + 24*n + 116 + (n^3 - 4*n^2 - 24*n + 12)*(-1)^n - (n^3 + 4*n^2 - 8*n - 108)*(-1)^((2*n + 5 - (-1)^n)/4) + (n^3 - 4*n^2 + 8*n - 20)*(-1)^((2*n + 7 + (-1)^n)/4))/2048. - _Luce ETIENNE_, Sep 02 2016
%t Flatten[Table[{n^2, n, n^3, n^4}, {n, 40}]] (* _Vincenzo Librandi_, Nov 25 2012 *)
%o (Magma) &cat[[n^2, n, n^3, n^4]: n in [1..20]]; // _Vincenzo Librandi_, Nov 25 2012
%o (PARI) lista(nn) = for(n=1, nn, print1(n^2, ", ", n, ", ", n^3, ", "n^4, ", ")); \\ _Jinyuan Wang_, Feb 28 2020
%Y Cf. A000463, A109588, A109594.
%K nonn,easy
%O 1,5
%A _Mohammad K. Azarian_, Sep 14 2005