OFFSET
5,2
COMMENTS
Rotations and reflections of a selection are regarded as different. For the number of congruence classes see A289232.
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 5..100
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = (n^10 -10*n^9 -85*n^8 +1160*n^7 +1345*n^6 -49162*n^5 +62145*n^4 +892140*n^3 -2198566*n^2 -5725008*n +18190440)/120.
G.f.: 3*x^6*(140 + 3496*x + 15761*x^2 + 1293*x^3 - 18129*x^4 + 3779*x^5 + 6103*x^6 - 1637*x^7 - 1139*x^8 + 413*x^9) / (1 - x)^11. - Colin Barker, Jul 01 2017
EXAMPLE
There are 420 ways to choose five 2 X 2 X 2 triangles (aaa, ..., eee) from a 6 X 6 X 6 point grid, for example:
. a
. . a a
. . . . d .
a a b b b d d c
c a d b e b b e c c
c c d d e e . . e e . .
Note: aaa, ..., eee are not distinguishable, they are denoted differently for a better perception of the 2 X 2 X 2 triangles only.
PROG
(PARI) concat(0, Vec(3*x^6*(140 + 3496*x + 15761*x^2 + 1293*x^3 - 18129*x^4 + 3779*x^5 + 6103*x^6 - 1637*x^7 - 1139*x^8 + 413*x^9) / (1 - x)^11 + O(x^40))) \\ Colin Barker, Jul 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Jul 01 2017
STATUS
approved