A237529 Number of ways to choose 4 points in an n X n X n triangular grid so that no 3 of them form a 2 X 2 X 2 subtriangle.

6, 156, 1191, 5565, 19620, 57351, 146391, 336951, 714555, 1417515, 2660196, 4763226, 8191911, 13604220, 21909810, 34341666, 52542036, 78664446, 115493685, 166585755, 236429886, 330634821, 456141681, 621465825, 836970225, 1115172981, 1471091706, 1922627616

Offset: 3

Author

Heinrich Ludwig, Feb 09 2014

Keywords

• nonn
• easy

Comments

All elements of the sequence are multiples of 3.

Links

• Heinrich Ludwig, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A234251, A234250.

Programs

Mathematica

LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{6,156,1191,5565,19620,57351,146391,336951,714555},40] (* Harvey P. Dale, Sep 29 2019 *)

PARI

Vec(-3*x^3*(2*x^6-11*x^5+21*x^4-14*x^3+x^2+34*x+2)/(x-1)^9 + O(x^100)) \\ Colin Barker, Feb 09 2014

Formula

a(n) = (n-1)*(n-2)*(n^6 + 7*n^5 + 13*n^4 - 7*n^3 - 230*n^2 - 408*n + 1152)/384.

G.f.: -3*x^3*(2*x^6 - 11*x^5 + 21*x^4 - 14*x^3 + x^2 + 34*x + 2) / (x-1)^9. - Colin Barker, Feb 09 2014