A160749 a(n) = (11*n^2 + 19*n + 10)/2.

5, 20, 46, 83, 131, 190, 260, 341, 433, 536, 650, 775, 911, 1058, 1216, 1385, 1565, 1756, 1958, 2171, 2395, 2630, 2876, 3133, 3401, 3680, 3970, 4271, 4583, 4906, 5240, 5585, 5941, 6308, 6686, 7075, 7475, 7886, 8308, 8741, 9185, 9640, 10106, 10583

Offset: 0

Author

N. J. A. Sloane, Nov 18 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, 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 (3,-3,1).

Crossrefs

Cf. A017437.

Programs

GAP

List([0..50], n-> (11*n^2+19*n+10)/2); # G. C. Greubel, Sep 18 2019

Magma

[(11*n^2+19*n+10)/2: n in [0..50]]; // Vincenzo Librandi, Sep 18 2011

Maple

seq((11*n^2+19*n+10)/2, n=0..50); # G. C. Greubel, Sep 18 2019

Mathematica

Table[(11n^2+19n+10)/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1}, {5,20,46}, 50] (* Harvey P. Dale, Nov 06 2014 *)

PARI

a(n)=(11*n^2+19*n+10)/2 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(11*n^2+19*n+10)/2 for n in (0..50)] # G. C. Greubel, Sep 18 2019

Formula

G.f.: (5+5*x+x^2)/(1-x)^3.

a(n) = a(n-1) + 11*n + 4 for n>0, a(0)=5. - Vincenzo Librandi, Sep 18 2011

E.g.f.: (10 + 30*x + 11*x^2)*exp(x)/2. - G. C. Greubel, Apr 26 2018