A343318 a(n) = (2^n + 1)^3.

8, 27, 125, 729, 4913, 35937, 274625, 2146689, 16974593, 135005697, 1076890625, 8602523649, 68769820673, 549957165057, 4398851866625, 35187593412609, 281487861809153, 2251851353686017, 18014604668698625, 144116012711149569, 1152924803144876033, 9223385231000600577

Offset

0,1

Comments

The number of vertices when starting with a cube (n=0) and iterating by dividing every cube into 8 equal cubes.

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (15,-70,120,-64).

Formula

G.f.: (8 - 93*x + 280*x^2 - 216*x^3)/(1 - 15*x + 70*x^2 - 120*x^3 + 64*x^4). - Stefano Spezia, Apr 12 2021

Example

a(2) = 125; since after iterating twice on the original cube, there are now 64 cubes inside. This 4 X 4 X 4 arrangement of cubes has 5*5=25 vertices on each face across the 5 slices, thus 125 vertices.

Mathematica

(2^Range[0, 25] + 1)^3 (* Wesley Ivan Hurt, Apr 11 2021 *)

Prog

(Python)
def A343318(n): return (2**n+1)**3 # Chai Wah Wu, Feb 03 2022

Crossrefs

a(n) = A000578(A000051(n)).

Sequence in context: A133042 A181361 A056570 * A165048 A066963 A067813

Adjacent sequences: A343315 A343316 A343317 * A343319 A343320 A343321

Keyword

nonn,easy

Author

Steve Bosze, Apr 11 2021

Status

approved