A210631 G.f. for Ehrhart quasi-polynomials for hyperplane arrangements of type F_4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 8, 10, 17, 21, 32, 39, 55, 66, 89, 105, 136, 159, 200, 231, 284, 325, 392, 445, 528, 595, 697, 780, 903, 1005, 1152, 1275, 1449, 1596, 1800, 1974, 2211, 2415, 2689, 2926, 3240, 3514, 3872, 4186, 4592, 4950, 5408, 5814, 6328, 6786, 7361, 7875, 8515, 9090, 9800, 10440

Offset: 0

Author

N. J. A. Sloane, Mar 25 2012

Keywords

• nonn
• easy

Links

• 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 (1,2,-1,-1,-2,0,2,1,1,-2,-1,1).

Crossrefs

Similar to A115264 but has different offset.

Programs

Mathematica

LinearRecurrence[{1,2,-1,-1,-2,0,2,1,1,-2,-1,1},{0,0,0,0,0,0,0,0,0,0,0,0,1},70] (* Harvey P. Dale, Oct 28 2015 *)

Formula

G.f.: x^12*f(1)*f(2)^2*f(3)*f(4) where f(k)=1/(1-x^k).

G.f.: x^12/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^4)). - Colin Barker, Jul 22 2013