A109614 n^3 followed by n followed by n^2.

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

Offset: 1

Author

Mohammad K. Azarian, Aug 30 2005

Keywords

• nonn
• easy
• look

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..3000
• Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).

Crossrefs

Cf. A000463.

Cf. A000578, A000027, A000290.

Cf. A010872.

Programs

Haskell

import Data.List (transpose)
a109614 n = a109614_list !! (n-1)
a109614_list = concat $ transpose
               [tail a000578_list, a000027_list, tail a000290_list]
-- Reinhard Zumkeller, Mar 14 2014

Mathematica

Table[{n^3,n,n^2},{n,20}]//Flatten (* or *) LinearRecurrence[{0,0,4,0,0,-6,0,0,4,0,0,-1},{1,1,1,8,2,4,27,3,9,64,4,16},60] (* Harvey P. Dale, Feb 25 2016 *)

Formula

From R. J. Mathar, Jun 26 2009: (Start)

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

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

a(n) = floor((n+2)/3)^((-3*(n mod 3)^2 + 5*(n mod 3) + 4)/2). - Luce ETIENNE, Mar 01 2018