OFFSET
2,3
COMMENTS
Rotations and reflections of placements are not counted. If they are to be counted see A239569.
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-7,3,6,0,-6,-3,7,0,-3,1)
FORMULA
a(n) = (n^6 + 3*n^5 - 39*n^4 + 10*n^3 + 456*n^2 - 1008*n + 576)/288 + IF(MOD(n, 2) = 1)*(3*n^2 - 5*n - 5)/32 + IF(MOD(n, 3) = 1)*2/9.
G.f.: -x^3*(2*x^9 +x^8 -8*x^7 -9*x^6 +3*x^5 +29*x^4 +24*x^3 +14*x^2 +3*x +1) / ((x -1)^7*(x +1)^3*(x^2 +x +1)). - Colin Barker, Mar 23 2014
EXAMPLE
There are a(4) = 6 non-equivalent ways to place 3 points on a triangular grid of side 4:
. X X X X X
. X . . . . . . . . . .
X . . X . X X . . X . . . X . . . .
. . X . . . . . . . X . . . . X . . . X X . . X
PROG
(PARI) concat(0, Vec(-x^3*(2*x^9 +x^8 -8*x^7 -9*x^6 +3*x^5 +29*x^4 +24*x^3 +14*x^2 +3*x +1)/((x -1)^7*(x +1)^3*(x^2 +x +1)) + O(x^100))) \\ Colin Barker, Mar 23 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Mar 23 2014
STATUS
approved