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%I #25 Sep 08 2022 08:46:17
%S 0,0,0,0,1,1,1,1,8,4,16,2,27,9,81,3,64,16,256,4,125,25,625,5,216,36,
%T 1296,6,343,49,2401,7,512,64,4096,8,729,81,6561,9,1000,100,10000,10,
%U 1331,121,14641,11,1728,144,20736,12,2197,169,28561,13,2744,196,38416,14,3375,225,50625,15
%N n^3 followed by n^2 followed by n^4 followed by n.
%H Colin Barker, <a href="/A276071/b276071.txt">Table of n, a(n) for n = 0..1000</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 - 1 + (-1)^n)/4))*(n^3 - 2*n^2 + 28*n + 40 + (n^3 - 2*n^2 - 4*n - 56)*(-1)^n - (n^3 - 10*n^2 - 4*n + 72)*(-1)^((2*n - 1 + (-1)^n)/4) - (n^3 - 10*n^2 + 28*n - 88)*(-1)^((2*n + 1 - (-1)^n)/4))/2048.
%F G.f.: x^4*(1 + x + x^2 + x^3 + 3*x^4 - x^5 + 11*x^6 - 3*x^7 - 3*x^8 - 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
%e Rectangular array with four columns begins:
%e . 0, 0, 0, 0;
%e . 1, 1, 1, 1;
%e . 8, 4, 16, 2;
%e . 27, 9, 81, 3;
%e . 64, 16, 256, 4;
%e . 125, 25, 625, 5;
%e . 216, 36, 1296, 6; ...
%t Flatten[Table[{n^3, n^2, n^4, n}, {n, 0, 20}]] (* _Bruno Berselli_, Aug 21 2016 *)
%o (PARI) concat(vector(4), Vec(x^4*(1+x+x^2+x^3+3*x^4-x^5+11*x^6-3*x^7-3*x^8-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^60))) \\ _Colin Barker_, Aug 18 2016
%o (Magma) &cat[[n^3,n^2,n^4,n]: n in [0..20]]; // _Bruno Berselli_, Aug 21 2016
%Y Cf. A110009.
%K nonn,easy,tabf
%O 0,9
%A _Luce ETIENNE_, Aug 18 2016
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