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%I #26 Sep 20 2023 14:42:21
%S 1,1,1,1,4,16,8,2,9,81,27,3,16,256,64,4,25,625,125,5,36,1296,216,6,49,
%T 2401,343,7,64,4096,512,8,81,6561,729,9,100,10000,1000,10,121,14641,
%U 1331,11,144,20736,1728,12,169,28561,2197,13,196,38416,2744,14,225
%N n^2 followed by n^4 followed by n^3 followed by n.
%H Vincenzo Librandi, <a href="/A110651/b110651.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+10*n^2+36*n+124+(n^3+2*n^2-12*n+20)*(-1)^n+(n^3+2*n^2+20*n-12)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+10*n^2+4*n-100)*(-1)^((2*n+7+(-1)^n)/4))/2048. - _Luce ETIENNE_, Sep 02 2016
%F G.f.: x*(1+x+x^2+x^3-x^4+11*x^5+3*x^6-3*x^7-x^8+11*x^9-3*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_, Sep 02 2016
%F a(n) = 5*a(n-4)-10*a(n-8)+10*a(n-12)-5*a(n-16)+a(n-20). - _Wesley Ivan Hurt_, Jun 09 2023
%t Flatten[Table[{n^2, n^4, n^3, n}, {n, 40}]](* _Vincenzo Librandi_, Feb 06 2013 *)
%t LinearRecurrence[{0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1},{1,1,1,1,4,16,8,2,9,81,27,3,16,256,64,4,25,625,125,5},60] (* _Harvey P. Dale_, Sep 20 2023 *)
%o (Magma) &cat[[n^2, n^4, n^3, n]: n in [1..20]]; // _Vincenzo Librandi_, Feb 06 2013
%o (PARI) Vec(x*(1+x+x^2+x^3-x^4+11*x^5+3*x^6-3*x^7-x^8+11*x^9-3*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^30)) \\ _Colin Barker_, Sep 02 2016
%Y Cf. A000463, A109588, A109594.
%K nonn,easy
%O 1,5
%A _Mohammad K. Azarian_, Sep 14 2005
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