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

1,5

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).

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

Maple

map(t -> (t, t^4, t^3, t^2), [$1..100]); # Robert Israel, Aug 15 2016

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 *)

Prog

(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

Crossrefs

Cf. A000463, A109588, A109594.

Sequence in context: A070654 A036164 A076536 * A232503 A348007 A025586

Adjacent sequences: A110006 A110007 A110008 * A110010 A110011 A110012

Keyword

nonn,easy

Author

Mohammad K. Azarian, Sep 02 2005

Status

approved