login
A239571
Number of ways to place 5 points on a triangular grid of side n so that no two of them are adjacent.
7
0, 0, 27, 999, 11565, 74811, 342042, 1239525, 3799488, 10259640, 25076952, 56552364, 119324403, 238062357, 452774595, 826245798, 1454229216, 2479147536, 4108199481, 6636929805, 10479498849, 16207085223, 24596072424, 36687908235, 53862785520, 77929575480
OFFSET
3,3
COMMENTS
Rotations and reflections of placements are counted. If they are to be ignored see A239575.
LINKS
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1)
FORMULA
a(n) = (n -3) * (n -4) * (n^8 +12*n^7 -58*n^6 -860*n^5 +2141*n^4 +23728*n^3 -61316*n^2 -244928*n +770880)/3840.
G.f.: -3*x^5*(40*x^8-185*x^7+198*x^6+213*x^5-243*x^4-638*x^3+687*x^2+234*x+9) / (x-1)^11. - Colin Barker, Mar 22 2014
MATHEMATICA
CoefficientList[Series[- 3 x^2 (40 x^8 - 185 x^7 + 198 x^6 + 213 x^5 - 243 x^4 - 638 x^3 + 687 x^2 + 234 x + 9)/(x - 1)^11, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 23 2014 *)
PROG
(PARI) concat([0, 0], Vec(-3*x^5*(40*x^8-185*x^7+198*x^6+213*x^5-243*x^4-638*x^3+687*x^2+234*x+9)/(x-1)^11 + O(x^100))) \\ Colin Barker, Mar 22 2014
(Magma) [(n^2-7*n+12)*(n^8+12*n^7-58*n^6-860*n^5+2141*n^4 +23728*n^3-61316*n^2-244928*n+770880)/3840: n in [3..40]]; // Vincenzo Librandi, Mar 23 2014
CROSSREFS
Cf. A239567, A239575, A239568 (2 points), A239569 (3 points), A239570 (4 points), A282998 (6 points).
Sequence in context: A129999 A132059 A292362 * A017019 A143366 A143705
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Mar 22 2014
STATUS
approved