A110485 n^2 followed by n followed by n^4 followed by n^3.
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, 7, 2401, 343, 64, 8, 4096, 512, 81, 9, 6561, 729, 100, 10, 10000, 1000, 121, 11, 14641, 1331, 144, 12, 20736, 1728, 169, 13, 28561, 2197, 196, 14, 38416, 2744, 225, 15
Offset: 1
Keywords
Programs
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Mathematica
Flatten[Table[{n^2,n,n^4,n^3},{n,20}]] (* Harvey P. Dale, Oct 24 2013 *)
Formula
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
From Chai Wah Wu, Jan 11 2020: (Start)
a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.
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)