OFFSET
0,2
COMMENTS
Ehrhart series for matroid K_4.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
P. Aluffi, Degrees of projections of rank loci, arXiv:1408.1702 [math.AG], 2014. ["After compiling the results of many explicit computations, we noticed that many of the numbers d_{n,r,S} appear in the existing literature in contexts far removed from the enumerative geometry of rank conditions; we owe this surprising (to us) observation to perusal of [Slo14]."]
Hyunsoo Cho, JiSun Huh, Hayan Nam, and Jaebum Sohn, Combinatorics on bounded free Motzkin paths and its applications, arXiv:2205.15554 [math.CO], 2022. (See p. 14.)
J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
D. C. Haws, Matroids [Broken link, Oct 30 2017]
D. C. Haws, Matroids [Copy on website of Matthias Koeppe]
D. C. Haws, Matroids [Cached copy, pdf file only]
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: (1 + 10*x + 20*x^2 + 10*x^3 + x^4)/(1-x)^5.
a(n) = 1 + 7*n*(n+1)*(n^2+n+2)/4. - R. J. Mathar, Dec 16 2009
E.g.f.: (1/4)*(7*x^4 + 56*x^3 + 112*x^2 + 56*x + 4)*exp(x). - G. C. Greubel, Apr 26 2018
MATHEMATICA
Table[(7*n^4 + 14*n^3 + 21*n^2 + 14*n + 4)/4, {n, 0, 30}] (* G. C. Greubel, Apr 26 2018 *)
PROG
(Magma) [1+7*n*(n+1)*(n^2+n+2)/4: n in [0..40]]; // Vincenzo Librandi, Sep 18 2011
(PARI) a(n)=7*n*(n+1)*(n^2+n+2)/4+1 \\ Charles R Greathouse IV, Apr 17 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 18 2009
STATUS
approved