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A110004 n followed by n^3 followed by n^4 followed by n^2.

%I A110004 #24 Jul 19 2024 15:03:40
%S A110004 1,1,1,1,2,8,16,4,3,27,81,9,4,64,256,16,5,125,625,25,6,216,1296,36,7,
%T A110004 343,2401,49,8,512,4096,64,9,729,6561,81,10,1000,10000,100,11,1331,
%U A110004 14641,121,12,1728,20736,144,13,2197,28561,169,14,2744,38416,196,15
%N A110004 n followed by n^3 followed by n^4 followed by n^2.
%H A110004 Vincenzo Librandi, <a href="/A110004/b110004.txt">Table of n, a(n) for n = 1..4000</a>
%H A110004 <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 A110004 a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+35*n+81-(n^3-n^2-29*n+49)*(-1)^n-(n^3-n^2+3*n-79)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+7*n^2+3*n-47)*(-1)^((2*n+7+(-1)^n)/4))/2048. - _Luce ETIENNE_, Sep 03 2016
%F A110004 From _Chai Wah Wu_, Jan 11 2020: (Start)
%F A110004 a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.
%F A110004 G.f.: x*(-x^15 - x^14 + x^13 + x^12 + x^11 - 11*x^10 + 3*x^9 - 3*x^8 + x^7 - 11*x^6 - 3*x^5 + 3*x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)
%t A110004 Table[n^{1, 3, 4, 2}, {n, 15}] // Flatten (* or *)
%t A110004 Table[(2 n + 3 - (-1)^n + 2 (-1)^((2 n + 5 - (-1)^n)/4)) (n^3 + 7 n^2 + 35 n + 81 - (n^3 - n^2 - 29 n + 49) (-1)^n - (n^3 - n^2 + 3 n - 79) (-1)^((2 n + 5 - (-1)^n)/4) - (n^3 + 7 n^2 + 3 n - 47) (-1)^((2 n + 7 + (-1)^n)/4))/2048, {n, 57}] (* _Michael De Vlieger_, Sep 03 2016 *)
%t A110004 LinearRecurrence[{0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1},{1,1,1,1,2,8,16,4,3,27,81,9,4,64,256,16,5,125,625,25},60] (* _Harvey P. Dale_, Jul 19 2024 *)
%o A110004 (Magma) [&cat[[n,n^3,n^4,n^2]: n in [1..20]]]; // _Vincenzo Librandi_, Sep 05 2016
%Y A110004 Cf. A000463, A109588, A109594.
%K A110004 nonn
%O A110004 1,5
%A A110004 _Mohammad K. Azarian_, Sep 02 2005