A110009 n followed by n^4 followed by n^2 followed by n^3.
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, 2401, 49, 343, 8, 4096, 64, 512, 9, 6561, 81, 729, 10, 10000, 100, 1000, 11, 14641, 121, 1331, 12, 20736, 144, 1728, 13, 28561, 169, 2197, 14, 38416, 196, 2744, 15, 50625
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1).
Programs
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Maple
map(t -> (t,t^4,t^3,t^2), [$1..100]); # Robert Israel, Aug 15 2016
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Mathematica
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 *) -
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
Formula
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
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