A110650 - OEIS

%I #23 Sep 08 2022 08:45:20

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

%T 2401,7,343,64,4096,8,512,81,6561,9,729,100,10000,10,1000,121,14641,

%U 11,1331,144,20736,12,1728,169,28561,13,2197,196,38416,14,2744,225,50625

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

%H Vincenzo Librandi, <a href="/A110650/b110650.txt">Table of n, a(n) for n = 1..8000</a>

%F a(n) = floor((n+3)/4)^((-8*(n mod 4)^3 + 33*(n mod 4)^2 - 31*(n mod 4) + 18)/6). - _Luce ETIENNE_, Apr 07 2018

%F From _Chai Wah Wu_, Jan 10 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 - 3*x^10 - 11*x^9 + x^8 - 3*x^7 + 3*x^6 - 11*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^4,n,n^3},{n,20}]] (* _Harvey P. Dale_, Oct 10 2012 *)

%o (Magma) &cat[[n^2, n^4, n, n^3]: n in [1..20]]; // _Vincenzo Librandi_, Nov 25 2012

%o (GAP) Flat(List([1..20],n->[n^2,n^4,n,n^3])); # _Muniru A Asiru_, Apr 08 2018

%Y Cf. A000463; A109588; A109594.

%Y Cf. A010873.

%K nonn,easy

%O 1,5

%A _Mohammad K. Azarian_, Sep 14 2005