A160829 - OEIS

%I #30 Sep 08 2022 08:45:45

%S 1,51,673,4287,17931,57321,152251,353333,740077,1430311,2590941,

%T 4450051,7310343,11563917,17708391,26364361,38294201,54422203,

%U 75856057,103909671,140127331,186309201,244538163,317207997,407052901,517178351

%N Expansion of (1 + 44*x + 337*x^2 + 612*x^3 + 305*x^4 + 40*x^5 + x^6)/(1 - x)^7.

%C Source: the De Loera et al. article and the Haws website listed in A160747.

%H G. C. Greubel, <a href="/A160829/b160829.txt">Table of n, a(n) for n = 0..10000</a>

%H J. A. De Loera, D. C. Haws and M. Koppe, <a href="https://arxiv.org/abs/0710.4346">Ehrhart Polynomials of Matroid Polytopes and Polymatroids</a>, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7), with a(0)=1, a(1)=51, a(2)=673, a(3)=4287, a(4)=17931, a(5)=57321, a(6)=152251. - _Harvey P. Dale_, Jun 21 2011

%F a(n) = (1/36)*(36 + 174*n + 391*n^2 + 513*n^3 + 442*n^4 + 213*n^5 + 67*n^6). - _Harvey P. Dale_, Jun 21 2011, corrected by _Eric Rowland_, Aug 15 2017

%p seq(coeff(series((1+44*x+337*x^2+612*x^3+305*x^4+40*x^5+x^6)/(1-x)^7, x,n+1),x,n),n=0..25); # _Muniru A Asiru_, Apr 29 2018

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,51,673,4287,17931,57321, 152251},30] (* or *) CoefficientList[Series[ (1+44x+337x^2+612x^3+ 305x^4+ 40x^5+x^6)/(1-x)^7,{x,0,30}],x] (* _Harvey P. Dale_, Jun 21 2011 *)

%o (PARI) x='x+O('x^99); Vec((1+44*x+337*x^2+612*x^3+305*x^4+40*x^5+x^6)/(1-x)^7) \\ _Altug Alkan_, Aug 16 2017

%o (Magma) [(1/36)*(36 + 174*n + 391*n^2 + 513*n^3 + 442*n^4 + 213*n^5 + 67*n^6): n in [0..30]]; // _G. C. Greubel_, Apr 28 2018

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Nov 18 2009