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A244502 Number of ways to place 4 points on an n X n X n triangular grid so that no pair of them has distance sqrt(3). 4
33, 378, 2190, 9110, 30300, 85563, 213293, 482085, 1006950, 1971185, 3655053, 6472533, 11017505, 18120840, 28919970, 44942618, 68206473, 101336700, 147703280, 211580280, 298329258, 414609113, 568614795, 770347395, 1031918240, 1367889723, 1795655703, 2335864415 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
COMMENTS
sqrt(3) is the second closest (Euclidean) distance for a pair of points in a triangular grid. For illustration see A244500.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = 1/384*n^8 + 1/96*n^7 - 13/64*n^6 + 5/48*n^5 + 875/128*n^4 - 2543/96*n^3 - 4141/96*n^2 + 3759/8*n - 837, for n >= 5.
G.f.: x^4*(10*x^9 - 30*x^8 + 130*x^6 - 333*x^5 + 444*x^4 - 236*x^3 + 24*x^2 - 81*x - 33) / (x - 1)^9. - Colin Barker, Jun 29 2014
MAPLE
A244502:=n->`if`(n=4, 33, 1/384*n^8 + 1/96*n^7 - 13/64*n^6 + 5/48*n^5 + 875/128*n^4 - 2543/96*n^3 - 4141/96*n^2 + 3759/8*n - 837); seq(A244502(n), n=4..30); # Wesley Ivan Hurt, Jun 30 2014
MATHEMATICA
CoefficientList[Series[(10*x^9 - 30*x^8 + 130*x^6 - 333*x^5 + 444*x^4 - 236*x^3 + 24*x^2 - 81*x - 33)/(x - 1)^9, {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 30 2014 *)
PROG
(PARI) Vec(x^4*(10*x^9-30*x^8+130*x^6-333*x^5+444*x^4-236*x^3+24*x^2-81*x-33)/(x-1)^9 + O(x^100)) \\ Colin Barker, Jun 29 2014
CROSSREFS
Sequence in context: A264282 A167963 A085742 * A202256 A324950 A252925
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Jun 29 2014
STATUS
approved

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Last modified March 29 03:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)