A273982 Number of little cubes visible around an n X n X n cube with a face on a table.

1, 8, 25, 52, 89, 136, 193, 260, 337, 424, 521, 628, 745, 872, 1009, 1156, 1313, 1480, 1657, 1844, 2041, 2248, 2465, 2692, 2929, 3176, 3433, 3700, 3977, 4264, 4561, 4868, 5185, 5512, 5849, 6196, 6553, 6920, 7297, 7684, 8081, 8488, 8905, 9332, 9769, 10216

Offset: 1

Author

Sébastien Dumortier, Jun 05 2016

Keywords

• nonn
• easy

Comments

There are fewer visible cubes on the bottom than on the top.

Examples

			a(3)=25 because around a 3 X 3 X 3 cube, when it's on a table, it's possible to see only 25 little cubes (8 on each of the 2 bottom layers and 9 on the top layer).
		

Links

• Leo Tavares, Illustration: Diamond Branches
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A005897, A168668, A000566.

Programs

Magma

[5*n^2-8*n+4: n in [1..60]]; // Vincenzo Librandi, Jun 06 2016

Maple

A273982:=n->5*n^2-8*n+4: seq(A273982(n), n=1..60); # Wesley Ivan Hurt, Oct 06 2017

Mathematica

Table[5 n^2 - 8 n + 4, {n, 46}] (* or *)
LinearRecurrence[{3, -3, 1}, {1, 8, 25}, 46] (* or *)
CoefficientList[Series[(-1 - 5 x - 4 x^2)/(-1 + x)^3, {x, 0, 45}], x] (* Michael De Vlieger, Oct 06 2017 *)

PARI

a(n) = 5*n^2 - 8*n + 4; \\ Altug Alkan, Oct 06 2017

Formula

a(n) = 5*n^2 - 8*n + 4.

a(n) = n^3 - (n-2)^3 - (n-2)^2. - Joerg Arndt, Jun 06 2016

a(n) = A168668(n-1) + 1. - Altug Alkan, Oct 06 2017

G.f.: (-1 - 5*x - 4*x^2)/(-1 + x)^3. - Michael De Vlieger, Oct 06 2017

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. - Wesley Ivan Hurt, Oct 06 2017

a(n) = A000566(n-1) + A000566(n), the sum of consecutive heptagonal numbers. - Charlie Marion, Jul 01 2021

a(n) = n^2 + 4*(n-1)^2. - Leo Tavares, Mar 24 2022

Extensions

a(2) corrected and entry edited by Andrey Zabolotskiy, Oct 06 2017