A210634 G.f. for Ehrhart quasi-polynomials for hyperplane arrangements of type E_6.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 9, 20, 42, 78, 139, 231, 372, 573, 861, 1254, 1791, 2499, 3432, 4629, 6162, 8085, 10492, 13455, 17094, 21503, 26832, 33201, 40795, 49764, 60333, 72687, 87096, 103785, 123075, 145236, 170646, 199626, 232617, 269997, 312277, 359898, 413448, 473438, 540540, 615342, 698608

Offset: 0

Author

N. J. A. Sloane, Mar 25 2012

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Andreas Blass, Bruce E. Sagan, Characteristic and Ehrhart polynomials, arXiv:math/9801008 [math.CO], 1998.
• Andreas Blass, Bruce E. Sagan, Characteristic and Ehrhart polynomials, J. Algebraic Combin. 7 (1998), no. 2, 115--126. MR1609889 (99c:05204)
• Index entries for linear recurrences with constant coefficients, signature (3,0,-7,3,6,0,-6,-3,7,0,-3,1).

Crossrefs

A164680 is similar but has a different offset.

Programs

Mathematica

LinearRecurrence[{3,0,-7,3,6,0,-6,-3,7,0,-3,1},{0,0,0,0,0,0,0,0,0,0,0,0,1},60] (* Harvey P. Dale, Mar 27 2025 *)

Formula

G.f.: x^12*f(1)^3*f(2)^3*f(3) where f(k)=1/(1-x^k).

G.f.: x^12/((1-x)^3*(1-x^2)^3*(1-x^3)). - Colin Barker, Jul 22 2013