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

1,4

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).

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

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 *)

Prog

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

Crossrefs

Cf. A000463.

Sequence in context: A246363 A319268 A277272 * A254788 A347669 A352812

Adjacent sequences: A109585 A109586 A109587 * A109589 A109590 A109591

Keyword

nonn,easy

Author

Mohammad K. Azarian, Aug 30 2005

Status

approved