A110009 - OEIS

%I #29 Aug 16 2016 13:14:18

%S 1,1,1,1,2,16,4,8,3,81,9,27,4,256,16,64,5,625,25,125,6,1296,36,216,7,

%T 2401,49,343,8,4096,64,512,9,6561,81,729,10,10000,100,1000,11,14641,

%U 121,1331,12,20736,144,1728,13,28561,169,2197,14,38416,196,2744,15,50625

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

%H Colin Barker, <a href="/A110009/b110009.txt">Table of n, a(n) for n = 1..1000</a>

%H <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 a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n-3-(-1)^n)/4))*(n^3+10*n^2+28*n+88+(n^3+10*n^2-4*n-72)*(-1)^n+(n^3+2*n^2-4*n+56)*(-1)^((2*n-3-(-1)^n)/4)-(n^3+2*n^2+28*n-40)*(-1)^((2*n-1+(-1)^n)/4))/2048. - _Luce ETIENNE_, Aug 15 2016

%F G.f.: x*(1+x+x^2+x^3-3*x^4+11*x^5-x^6+3*x^7+3*x^8+11*x^9-x^10-3*x^11-x^12+x^13+x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5). - _Colin Barker_, Aug 15 2016

%p map(t -> (t,t^4,t^3,t^2), [$1..100]); # _Robert Israel_, Aug 15 2016

%t Flatten[Table[{n,n^4,n^2,n^3},{n,20}]] (* or *) Flatten[ With[ {c=Range[20]}, Thread[{c,c^4,c^2,c^3}]]] (* _Harvey P. Dale_, Mar 28 2012 *)

%o (PARI) Vec(x*(1+x+x^2+x^3-3*x^4+11*x^5-x^6+3*x^7+3*x^8+11*x^9-x^10-3*x^11-x^12+x^13+x^14-x^15)/((1-x)^5*(1+x)^5*(1+x^2)^5) + O(x^60)) \\ _Colin Barker_, Aug 15 2016

%Y Cf. A000463, A109588, A109594.

%K nonn,easy

%O 1,5

%A _Mohammad K. Azarian_, Sep 02 2005