login
A272130
a(n) = 16*n^3 + 10*n^2 + 4*n + 1.
2
1, 31, 177, 535, 1201, 2271, 3841, 6007, 8865, 12511, 17041, 22551, 29137, 36895, 45921, 56311, 68161, 81567, 96625, 113431, 132081, 152671, 175297, 200055, 227041, 256351, 288081, 322327, 359185, 398751, 441121, 486391, 534657, 586015, 640561, 698391
OFFSET
0,2
LINKS
M. Beck, J. A. De Loera, M. Develin, J. Pfeifle and R. P. Stanley, Coefficients and roots of Ehrhart Polynomials, Contemp. Math. 374 (2005), 15-36, page 19.
FORMULA
O.g.f.: (1+27*x+59*x^2+9*x^3)/(1-x)^4.
E.g.f.: (1+30*x+58*x^2+16*x^3)*exp(x).
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3.
a(n) = A158187(n) + A144965(n).
MAPLE
A272130:=n->16*n^3+10*n^2+4*n+1: seq(A272130(n), n=0..50); # Wesley Ivan Hurt, Apr 22 2016
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {1, 31, 177, 535}, 50]
CoefficientList[Series[(1 + 27*x + 59*x^2 + 9*x^3)/(1 - x)^4, {x, 0, 30}], x] (* Wesley Ivan Hurt, Apr 22 2016 *)
PROG
(Magma) [16*n^3+10*n^2+4*n+1: n in [0..50]];
(PARI) vector(100, n, n--; 16*n^3+10*n^2+4*n+1) \\ Altug Alkan, Apr 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 21 2016
STATUS
approved