A005897 (Points on surface of cube)

[all at abouthugo.de]

J. A. Sloane" <njas at research.att.com> schrieb am 15.07.2003, 22:01:49:
> The entry is , in full,
> 
> %I A005897 M4497
> %S A005897 1,8,26,56,98,152,218,296,386,488,602,728,866,1016,1178,1352,1538,
[...]
> %N A005897 Points on surface of cube: 6n^2 + 2 (coordination sequence for b.c.c. lattice).
[...]
> 
> To get 6n^2 + 2 (for n>0) take a cube, divide
> each edge into n+1 equally spaced points
> (so for n = 2 we get *----*----* )
> and fill in each face with a square mesh through these
> points. The total number of points is
> 8 + 12(n-1) + 6(n-1)^2 = 6n^2+2.
> 
> NJAS

Neil, SeqFans,

it was not obvious to me that the number of
sub-cubes cut (not just touched in an edge or
face) is equal to the number of lattice points
on the surface of the subdivided cube. If this
is true, than it should be added as a comment
to A005897. Or is there a new sequence?

To get an idea, I also checked A008574, which is
the analoguous 2-d sequence:
http://www.research.att.com/projects/OEIS?Anum=A008574
%I A008574
%S A008574 1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,
%T A008574 76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,
%U A008574 136,140,144,148,152,156,160,164,168,172,176,180,184
%N A008574 Expansion of (1+x)^2 / (1-x)^2 (coordination sequence for
square lattice).
%C A008574 Susceptibility series H_1 for 2-dimensional Ising model
(divided by 2).
%C A008574 Also the Engel expansion of exp^(1/4); cf. A006784 for the
Engel expansion definition - 
Benoit Cloitre (abcloitre(AT)wanadoo.fr), Mar 03 2002

This description sounds very complicated, but in
fact it's just number of lattice points on the
circumference of an n*n square=4*n. (excluding
the singular first sequence term, otherwise
"multiples of 4": A008586)
And it's also the number of squares cut (not just
touched) by a circle around the center of the
large square with radius n/2.

Is that correct?

Hugo