%I
%S 60,120,204,312,444,600,780,984,1212,1464,1740,2040,2364,2712,3084,
%T 3480,3900,4344,4812,5304,5820,6360,6924,7512,8124,8760,9420,10104,
%U 10812,11544,12300,13080,13884,14712,15564,16440,17340,18264,19212,20184,21180,22200,23244
%N a(n) is the total surface area of a hollow cubic block (defined as a block with a shell thickness of 1 cube) where n is the edge length of the removed volume.
%C A cubic block is made of (n+2)^3 unit cubes, beginning with n=1. A hollow cubic block is a cubic block with all internal cubes removed (making its thickness 1), so its volume is (n+2)^3n^3. The external edge length of a hollow cube is n+2, while the internal hollow volume edge length is n. The external surface area is 6*(n+2)^2 while the internal surface area is 6*n^2, therefore the total surface area is 6*(n+2)^2+6*n^2.
%H Colin Barker, <a href="/A309842/b309842.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,1).
%F a(n) = 12*n^2 + 24*n + 24.
%F a(n) = A033581(n) + A033581(n+2).
%F a(n) = 12*A002522(n+1).
%F From _Colin Barker_, Nov 24 2019: (Start)
%F G.f.: 12*x*(5  5*x + 2*x^2) / (1  x)^3.
%F a(n) = 3*a(n1)  3*a(n2) + a(n3) for n>3.
%F (End)
%e The minimum cubic block that can be hollow is of volume 27, it is made hollow by removing the center cube. The external surface area is 3*3*6=54, the internal surface area is 1*1*6=6 so the total area is 60. a(1) = 60.
%o (PARI) Vec(12*x*(5  5*x + 2*x^2) / (1  x)^3 + O(x^60)) \\ _Colin Barker_, Nov 24 2019
%Y Cf. A002522, A033581.
%K nonn,easy
%O 1,1
%A _Anthony D. Santamaria_, Nov 18 2019
