%I #13 Sep 08 2022 08:46:16

%S 1,43,369,1507,4273,9771,19393,34819,58017,91243,137041,198243,277969,

%T 379627,506913,663811,854593,1083819,1356337,1677283,2052081,2486443,

%U 2986369,3558147,4208353,4943851,5771793,6699619,7735057,8886123,10161121,11568643

%N a(n) = 12*n^4 + 16*n^3 + 10*n^2 + 4*n + 1.

%H M. Beck, J. A. De Loera, M. Develin, J. Pfeifle and R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/papers/ehrhart.pdf">Coefficients and roots of Ehrhart Polynomials</a>, Contemp. Math. 374 (2005), 15-36, page 19.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F O.g.f.: (1+38*x+164*x^2+82*x^3+3*x^4)/(1-x)^5.

%F E.g.f.: (1+42*x+142*x^2+88*x^3+12*x^4)*exp(x).

%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.

%F a(n) mod 4 = a(n) mod 8 = A010684(n). - _Wesley Ivan Hurt_, Apr 22 2016

%p A272124:=n->(12*n^4 + 16*n^3 + 10*n^2 + 4*n + 1): seq(A272124(n), n=0..60); # _Wesley Ivan Hurt_, Apr 22 2016

%t LinearRecurrence[{5, -10, 10, -5, 1}, {1, 43, 369, 1507, 4273}, 50]

%t CoefficientList[Series[(1 + 38*x + 164*x^2 + 82*x^3 + 3*x^4)/(1 - x)^5, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Apr 22 2016 *)

%o (Magma) [12*n^4+16*n^3+10*n^2+4*n+1: n in [0..50]]

%o (PARI) vector(100, n, n--; 12*n^4+16*n^3+10*n^2+4*n+1) \\ _Altug Alkan_, Apr 22 2016

%Y Cf. A010684, A272039.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Apr 21 2016