A237530 Number of non-equivalent (mod D_3) ways to choose three points in an n X n X n triangular grid so that they do not form a 2 X 2 X 2 subtriangle.

0, 4, 22, 82, 231, 566, 1216, 2410, 4428, 7712, 12780, 20392, 31409, 47032, 68594, 97878, 136836, 187998, 254100, 338602, 445213, 578524, 743424, 945860, 1192126, 1489768, 1846734, 2272430, 2776725, 3371170, 4067840, 4880734, 5824442, 6915732, 8172036, 9613236

Offset: 2

Author

Heinrich Ludwig, Feb 13 2014

Keywords

• nonn
• easy

Comments

Without the restriction "non-equivalent (mod D_3)" the numbers are given by A234250.

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)

Crossrefs

Cf. A234250, A234247.

Programs

Mathematica

LinearRecurrence[{3,0,-7,3,6,0,-6,-3,7,0,-3,1},{0,4,22,82,231,566,1216,2410,4428,7712,12780,20392},40] (* Harvey P. Dale, Dec 09 2021 *)

Formula

a(n) = (n^6 + 3*n^5 - 3*n^4 + 10*n^3 - 48*n^2 + IF(n==1 mod 2)*(27*n^2 - 45*n - 9) + IF(n==1 mod 3)*64)/288.

G.f.: x^3*(x^7-x^6-2*x^5-15*x^4-13*x^3-16*x^2-10*x-4) / ((x-1)^7*(x+1)^3*(x^2+x+1)). - Colin Barker, Feb 14 2014