A127148 Q(n,6), where Q(m,k) is defined in A127080 and A127137.

-120, -15, 48, 75, 72, 45, 0, -57, -120, -183, -240, -285, -312, -315, -288, -225, -120, 33, 240, 507, 840, 1245, 1728, 2295, 2952, 3705, 4560, 5523, 6600, 7797, 9120, 10575, 12168, 13905, 15792, 17835, 20040, 22413, 24960, 27687, 30600, 33705, 37008, 40515, 44232, 48165

Offset: 0

Author

N. J. A. Sloane, Mar 24 2007

Keywords

• sign
• easy

References

• V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

A row of A127080.

Programs

GAP

List([0..50], n-> n^3 -24*n^2 +128*n -120); # G. C. Greubel, Aug 12 2019

Magma

[n^3 -24*n^2 +128*n -120: n in [0..50]]; // G. C. Greubel, Aug 12 2019

Maple

seq(n^3 -24*n^2 +128*n -120, n=0..50); # G. C. Greubel, Aug 12 2019

Mathematica

Table[n^3-24n^2+128n-120,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{-120,-15,48,75},50] (* Harvey P. Dale, Oct 22 2013 *)

PARI

Vec(3*(91*x^3-204*x^2+155*x-40)/(x-1)^4 + O(x^50)) \\ Colin Barker, Nov 11 2014

Sage

[n^3 -24*n^2 +128*n -120 for n in (0..50)] # G. C. Greubel, Aug 12 2019

Formula

a(n) = n^3 -24*n^2 +128*n -120.

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), a(0)=-120, a(1)=-15, a(2)=48, a(3)=75. - Harvey P. Dale, Oct 22 2013

G.f.: (-3)*(40-155*x+204*x^2-91*x^3)/(1-x)^4. - Colin Barker, Nov 11 2014

E.g.f.: (-120 + 105*x - 21*x^2 + x^3)*exp(x). - G. C. Greubel, Aug 12 2019