A160829 Expansion of (1 + 44*x + 337*x^2 + 612*x^3 + 305*x^4 + 40*x^5 + x^6)/(1 - x)^7.

1, 51, 673, 4287, 17931, 57321, 152251, 353333, 740077, 1430311, 2590941, 4450051, 7310343, 11563917, 17708391, 26364361, 38294201, 54422203, 75856057, 103909671, 140127331, 186309201, 244538163, 317207997, 407052901, 517178351

Offset: 0

Author

N. J. A. Sloane, Nov 18 2009

Keywords

• nonn

Comments

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

Links

• G. C. Greubel, 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, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Programs

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

Maple

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

Mathematica

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 *)

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

Formula

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

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