OFFSET
3,4
COMMENTS
Rotations and reflections of placements are counted. If they are to be ignored, see A279446.
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 3..1000
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 + 6*n^11 - 195*n^10 - 670*n^9 + 17455*n^8 + 13426*n^7 - 836249*n^6 + 1252990*n^5 + 19599884*n^4 - 68542552*n^3 - 131400416*n^2 + 974223360*n - 1308856320)/46080 for n>=4.
G.f.: x^5*(1 + 340*x + 7720*x^2 + 21439*x^3 - 12927*x^4 - 27265*x^5 + 28385*x^6 - 6252*x^7 - 116*x^8 - 2365*x^9 + 1787*x^10 - 352*x^11) / (1 - x)^13. - Colin Barker, Feb 26 2017
EXAMPLE
There is a(5) = 1 way to place 6 points on a triangular grid of side n = 5:
X
. .
X . X
. . . .
X . X . X
MAPLE
A282998:=n->(n^12 + 6*n^11 - 195*n^10 - 670*n^9 + 17455*n^8 + 13426*n^7 - 836249*n^6 + 1252990*n^5 + 19599884*n^4 - 68542552*n^3 - 131400416*n^2 + 974223360*n - 1308856320)/46080: 0, seq(A282998(n), n=4..30); # Wesley Ivan Hurt, Apr 10 2017
MATHEMATICA
Drop[CoefficientList[Series[(x^5 * (1 + 340 * x + 7720 * x^2 + 21439 * x^3 - 12927 * x^4 - 27265 * x^5 + 28385 * x^6 - 6252 * x^7 - 116 * x^8 - 2365 * x^9 + 1787 * x^10 - 352 * x^11) / (1 - x)^13 ), {x, 0, 27}], x], 3] (* Indranil Ghosh, Feb 26 2017, from the g.f. by Colin Barker *)
PROG
(PARI) concat(vector(2), Vec(x^5*(1 + 340*x + 7720*x^2 + 21439*x^3 - 12927*x^4 - 27265*x^5 + 28385*x^6 - 6252*x^7 - 116*x^8 - 2365*x^9 + 1787*x^10 - 352*x^11) / (1 - x)^13 + O(x^30))) \\ Colin Barker, Feb 26 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Feb 26 2017
STATUS
approved