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A289227 Number of ways to select 6 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle. 7
0, 76, 10956, 371016, 4988324, 39302784, 218633416, 952344088, 3460482612, 10932805668, 30901640212, 79762409256, 190898410020, 428596770008, 910935932112, 1846146025240, 3588666200596, 6723331905852, 12188915557404, 21455723224456, 36776237135268, 61533021405936 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,2
COMMENTS
Rotations and reflections of a selection are regarded as different.
LINKS
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
Sequence in context: A184290 A093238 A185984 * A028480 A229413 A111682
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Jul 01 2017
STATUS
approved

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Last modified March 4 12:45 EST 2024. Contains 370532 sequences. (Running on oeis4.)