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

%I A160749 #31 Jan 08 2025 10:29:32
%S A160749 5,20,46,83,131,190,260,341,433,536,650,775,911,1058,1216,1385,1565,
%T A160749 1756,1958,2171,2395,2630,2876,3133,3401,3680,3970,4271,4583,4906,
%U A160749 5240,5585,5941,6308,6686,7075,7475,7886,8308,8741,9185,9640,10106,10583
%N A160749 a(n) = (11*n^2 + 19*n + 10)/2.
%H A160749 Vincenzo Librandi, <a href="/A160749/b160749.txt">Table of n, a(n) for n = 0..10000</a>
%H A160749 J. A. De Loera, D. C. Haws and M. Koppe, <a href="http://arxiv.org/abs/0710.4346">Ehrhart Polynomials of Matroid Polytopes and Polymatroids</a>, Discrete Comput. Geom., 42 (2009), 670-702.
%H A160749 D. C. Haws, <a href="http://www.math.ucdavis.edu/~haws/Matroids/">Matroids</a> [Broken link, Oct 30 2017]
%H A160749 D. C. Haws, <a href="https://www.math.ucdavis.edu/~mkoeppe/art/Matroids/">Matroids</a> [Copy on website of Matthias Koeppe]
%H A160749 D. C. Haws, <a href="/A160747/a160747.pdf">Matroids</a> [Cached copy, pdf file only]
%H A160749 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A160749 G.f.: (5+5*x+x^2)/(1-x)^3.
%F A160749 a(n) = a(n-1) + 11*n + 4 for n>0, a(0)=5. - _Vincenzo Librandi_, Sep 18 2011
%F A160749 E.g.f.: (10 + 30*x + 11*x^2)*exp(x)/2. - _G. C. Greubel_, Apr 26 2018
%p A160749 seq((11*n^2+19*n+10)/2, n=0..50); # _G. C. Greubel_, Sep 18 2019
%t A160749 Table[(11n^2+19n+10)/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1}, {5,20,46}, 50] (* _Harvey P. Dale_, Nov 06 2014 *)
%o A160749 (Magma) [(11*n^2+19*n+10)/2: n in [0..50]]; // _Vincenzo Librandi_, Sep 18 2011
%o A160749 (PARI) a(n)=(11*n^2+19*n+10)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A160749 (Sage) [(11*n^2+19*n+10)/2 for n in (0..50)] # _G. C. Greubel_, Sep 18 2019
%o A160749 (GAP) List([0..50], n-> (11*n^2+19*n+10)/2); # _G. C. Greubel_, Sep 18 2019
%Y A160749 Cf. A017437.
%K A160749 nonn,easy
%O A160749 0,1
%A A160749 _N. J. A. Sloane_, Nov 18 2009