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n^2 followed by n followed by n^4 followed by n^3.
1

%I #18 Jan 11 2020 06:41:19

%S 1,1,1,1,4,2,16,8,9,3,81,27,16,4,256,64,25,5,625,125,36,6,1296,216,49,

%T 7,2401,343,64,8,4096,512,81,9,6561,729,100,10,10000,1000,121,11,

%U 14641,1331,144,12,20736,1728,169,13,28561,2197,196,14,38416,2744,225,15

%N n^2 followed by n followed by n^4 followed by n^3.

%F a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+19*n+113-(n^3-n^2+19*n-15)*(-1)^n-(n^3+7*n^2-13*n-111)*(-1)^((2*n+5-(-1)^n)/4)-(n^3-n^2-13*n+17)*(-1)^((2*n+7+(-1)^n)/4))/2048. - _Luce ETIENNE_, Sep 01 2016

%F From _Chai Wah Wu_, Jan 11 2020: (Start)

%F 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 G.f.: x*(x^15 - x^14 + x^13 - x^12 + 3*x^11 - 11*x^10 - 3*x^9 + x^8 - 3*x^7 - 11*x^6 + 3*x^5 + x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)

%t Flatten[Table[{n^2,n,n^4,n^3},{n,20}]] (* _Harvey P. Dale_, Oct 24 2013 *)

%Y Cf. A000463, A109588, A109594.

%K nonn

%O 1,5

%A _Mohammad K. Azarian_, Sep 14 2005