A167554 The second left hand column of triangle A167552.

-2, -5, -7, -6, 0, 13, 35, 68, 114, 175, 253, 350, 468, 609, 775, 968, 1190, 1443, 1729, 2050, 2408, 2805, 3243, 3724, 4250, 4823, 5445, 6118, 6844, 7625, 8463, 9360, 10318, 11339, 12425, 13578, 14800, 16093, 17459, 18900, 20418

Offset: 2

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Equals the second left hand column of A167552.

Other left hand columns are A005408, A167555, A168302 and A168303.

Programs

Mathematica

Table[(1/6)*(2*n^3 - 15*n^2 + 19*n - 6), {n,2,100}] (* or *) LinearRecurrence[{4,-6,4,-1}, {-2, -5, -7, -6}, 100] (* G. C. Greubel, Jun 15 2016 *)

Formula

a(n) = (2*n^3 - 15*n^2 + 19*n - 6)/3!.

G.f.: (z^2 + 3*z - 2)/(z-1)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) - 3*a(n-1) + 3*a(n-2) - a(n-3) = 2*1.