A110653 n^2 followed by n^3 followed by n followed by n^4.
1, 1, 1, 1, 4, 8, 2, 16, 9, 27, 3, 81, 16, 64, 4, 256, 25, 125, 5, 625, 36, 216, 6, 1296, 49, 343, 7, 2401, 64, 512, 8, 4096, 81, 729, 9, 6561, 100, 1000, 10, 10000, 121, 1331, 11, 14641, 144, 1728, 12, 20736, 169, 2197, 13, 28561, 196, 2744, 14, 38416, 225, 3375
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..4000
Programs
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Magma
&cat[[n^2, n^3, n, n^4]: n in [1..20]]; // Vincenzo Librandi, Feb 06 2013
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Mathematica
Flatten[Table[{n^2, n^3, n, n^4}, {n, 40}]] (* Vincenzo Librandi, Feb 06 2013 *)
Formula
a(n) = floor((n+3)/4)^((-2*(n mod 4)^3+9*(n mod 4)^2 - 11*(n mod 4) + 8)/2). - Luce ETIENNE, Apr 07 2018
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 - 11*x^11 - 3*x^10 + 3*x^9 + x^8 - 11*x^7 + 3*x^6 - 3*x^5 + x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)