OFFSET
5,2
COMMENTS
Rotations and reflections of a selection are regarded as different.
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 5..100
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
a(n) = (n^12 -12*n^11 -129*n^10 +2090*n^9 +3985*n^8 -142832*n^7 +152809*n^6 +4752598*n^5 -12392266*n^4 -76011076*n^3 +274393360*n^2 +455879232*n -2015187840)/720 for n>=6.
G.f.: 4*x^6*(19 + 2492*x + 58629*x^2 + 249487*x^3 + 78686*x^4 - 397088*x^5 + 93163*x^6 + 160960*x^7 - 77014*x^8 - 10728*x^9 + 4312*x^10 + 5013*x^11 - 1611*x^12) / (1 - x)^13. - Colin Barker, Jul 01 2017
EXAMPLE
There are 76 ways to choose six 2 X 2 X 2 triangles (aaa, ..., fff) from a 6 X 6 X 6 point grid, for example:
a a
a a a a
. . . b . c
b b c c b b c c
d b e c f d . e . f
d d e e f f d d e e f f
Note: aaa, ..., fff 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(4*x^6*(19 + 2492*x + 58629*x^2 + 249487*x^3 + 78686*x^4 - 397088*x^5 + 93163*x^6 + 160960*x^7 - 77014*x^8 - 10728*x^9 + 4312*x^10 + 5013*x^11 - 1611*x^12) / (1 - x)^13 + O(x^40))) \\ Colin Barker, Jul 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Jul 01 2017
STATUS
approved