OFFSET
2,3
COMMENTS
Rotations and reflections of a selection are regarded as different. For the number of congruence classes see A117662(n-1).
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 2..100
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (n^4 -4*n^3 -7*n^2 +46*n -48)/2 for n>=2.
From Colin Barker, Jun 28 2017: (Start)
G.f.: 6*x^4*(2 - x)*(1 + x) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
(End)
EXAMPLE
There are 12 ways to choose two 2 X 2 X 2 triangles (xxx) from a 4 X 4 X 4 point grid, for example:
x x x
x x x x x x
. x x x . . . x .
. . x . x x . . . x x .
The other nine selections are reflections or rotations of these three.
PROG
(PARI) Vec(6*x^4*(2 - x)*(1 + x) / (1 - x)^5 + O(x^60)) \\ Colin Barker, Jun 28 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Jun 28 2017
STATUS
approved