A234250 Number of ways to choose 3 points in an n X n X n triangular grid so that they do not form a 2 X 2 X 2 triangle.

0, 16, 111, 439, 1305, 3240, 7091, 14126, 26154, 45660, 75955, 121341, 187291, 280644, 409815, 585020, 818516, 1124856, 1521159, 2027395, 2666685, 3465616, 4454571, 5668074, 7145150, 8929700, 11070891, 13623561, 16648639, 20213580, 24392815, 29268216, 34929576

Offset: 2

Author

Heinrich Ludwig, Feb 04 2014

Keywords

• nonn
• easy

Links

• Heinrich Ludwig, Table of n, a(n) for n = 2..999
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1)

Programs

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,16,111,439,1305,3240,7091},40] (* Harvey P. Dale, Mar 09 2019 *)

PARI

Vec(x^3*(x^4-3*x^3+2*x^2+x-16)/(x-1)^7 + O(x^100)) \\ Colin Barker, Feb 05 2014

Formula

a(n) = (n - 1)*(n - 2)*(n^4 + 6*n^3 + 13*n^2 + 16*n - 24)/48.

G.f.: x^3*(x^4-3*x^3+2*x^2+x-16) / (x-1)^7. - Colin Barker, Feb 05 2014