A109595 n^3 followed by n^2 followed by n.

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

Offset

1,4

Links

Table of n, a(n) for n=1..60.

Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).

Formula

a(n) = floor((n+2)/3)^((-3*(n mod 3)^2+7*(n mod 3)+2)/2). - Luce ETIENNE, Mar 01 2018

From Elmo R. Oliveira, Jul 01 2026: (Start)

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

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

Mathematica

Flatten[Table[{n^3, n^2, n}, {n, 20}]] (* Harvey P. Dale, Aug 22 2014 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 4, 0, 0, -6, 0, 0, 4, 0, 0, -1}, {1, 1, 1, 8, 4, 2, 27, 9, 3, 64, 16, 4}, 60] (* Harvey P. Dale, Aug 22 2014 *)

Prog

(Python)
def A109595(n): return n//3 if (m:=n%3)==0 else (n//3+1)**3 if m==1 else (n//3+1)**2 # Chai Wah Wu, Jul 01 2026

Crossrefs

Cf. A000463, A010872.

Cf. A000290, A000578.

Sequence in context: A382004 A337170 A050135 * A256782 A071832 A396256

Adjacent sequences: A109592 A109593 A109594 * A109596 A109597 A109598

Keyword

nonn,easy

Author

Mohammad K. Azarian, Aug 30 2005

Status

approved