A272124 a(n) = 12*n^4 + 16*n^3 + 10*n^2 + 4*n + 1.
1, 43, 369, 1507, 4273, 9771, 19393, 34819, 58017, 91243, 137041, 198243, 277969, 379627, 506913, 663811, 854593, 1083819, 1356337, 1677283, 2052081, 2486443, 2986369, 3558147, 4208353, 4943851, 5771793, 6699619, 7735057, 8886123, 10161121, 11568643
Offset: 0
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.
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[12*n^4+16*n^3+10*n^2+4*n+1: n in [0..50]];
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Maple
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
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Mathematica
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 43, 369, 1507, 4273}, 50] 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 *) -
PARI
vector(100, n, n--; 12*n^4+16*n^3+10*n^2+4*n+1) \\ Altug Alkan, Apr 22 2016
Formula
O.g.f.: (1+38*x+164*x^2+82*x^3+3*x^4)/(1-x)^5.
E.g.f.: (1+42*x+142*x^2+88*x^3+12*x^4)*exp(x).
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.
a(n) mod 4 = a(n) mod 8 = A010684(n). - Wesley Ivan Hurt, Apr 22 2016