A109588 n followed by n^2 followed by n^3.

1, 1, 1, 2, 4, 8, 3, 9, 27, 4, 16, 64, 5, 25, 125, 6, 36, 216, 7, 49, 343, 8, 64, 512, 9, 81, 729, 10, 100, 1000, 11, 121, 1331, 12, 144, 1728, 13, 169, 2197, 14, 196, 2744, 15, 225, 3375, 16, 256, 4096, 17, 289, 4913, 18, 324, 5832, 19, 361, 6859, 20, 400, 8000

Offset: 1

Author

Mohammad K. Azarian, Aug 30 2005

Keywords

• nonn
• easy

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).

Crossrefs

Cf. A000463.

Programs

GAP

Flat(List([1..20],n->[n,n^2,n^3])); # Muniru A Asiru, Sep 12 2018

Maple

seq(seq(n^k, k=1..3), n=1..20); # Zerinvary Lajos, Jun 29 2007

Mathematica

CoefficientList[Series[(1 + x + x^2 - 2*x^3 + 4*x^5 + x^6 - x^7 + x^8)/((1 - x)^4*(1 + x + x^2)^4), {x, 0, 20}], x] (* Stefano Spezia, Sep 12 2018 *)
Table[{n,n^2,n^3},{n,20}]//Flatten (* or *) LinearRecurrence[{0,0,4,0,0,-6,0,0,4,0,0,-1},{1,1,1,2,4,8,3,9,27,4,16,64},60] (* Harvey P. Dale, Jan 10 2020 *)

Formula

From R. J. Mathar, Mar 30 2009: (Start)

a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) - a(n-12).

a(3*k+1) = k+1, a(3*k+2) = A000290(k+1), a(3*k+3) = A000578(k+1).

G.f.: x*(1 + x + x^2 - 2*x^3 + 4*x^5 + x^6 - x^7 + x^8)/((1 - x)^4*(1 + x + x^2)^4). (End)

a(n) = floor((n + 2)/3)*((1 - (-1)^(2^(n + 2 - 3*floor((n + 2)/3))))/2 + floor((n + 2)/3)*(1 - (-1)^(2^(n + 1 - 3*floor((n + 1)/3))))/2 + (floor((n + 2)/3))^2*(1 - (-1)^(2^(n - 3*floor(n/3))))/2). - Luce ETIENNE, Dec 16 2014

E.g.f.: ((2*x^3 + 3*x^2 + 8*x - 21)*exp(-x/2)*cos(sqrt(3)*x/2) + (3*x^2 + 8*x + 15)*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2) + (x^3 + 6*x^2 + 19*x + 21)*exp(x))/81. - Robert Israel, Dec 17 2014