A026054 dot product (n,n-1,...2,1).(3,4,...,n,1,2).

13, 28, 50, 80, 119, 168, 228, 300, 385, 484, 598, 728, 875, 1040, 1224, 1428, 1653, 1900, 2170, 2464, 2783, 3128, 3500, 3900, 4329, 4788, 5278, 5800, 6355, 6944, 7568, 8228, 8925, 9660, 10434, 11248, 12103, 13000, 13940, 14924, 15953, 17028, 18150, 19320, 20539, 21808, 23128, 24500, 25925

Offset: 3

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A023551.

Column 2 of triangle A094415.

Essentially the same as A060488. - Vladeta Jovovic, Jun 15 2006

Programs

GAP

List([0..60], n-> n*(n^2+9*n-10)/6); # G. C. Greubel, Oct 30 2019

Magma

[n*(n^2+9*n-10)/6: n in [3..60]]; // Vincenzo Librandi, Oct 17 2013

Magma

[n*(n^2+9*n-10)/6: n in [0..60]]; // G. C. Greubel, Oct 30 2019

Maple

seq(n*(n^2+9*n-10)/6, n=3..60); # G. C. Greubel, Oct 30 2019

Mathematica

Table[Range[n,1,-1].RotateLeft[Range[n],2],{n,3,60}] (* or *) LinearRecurrence[ {4,-6,4,-1},{13,28,50,80},60] (* Harvey P. Dale, Oct 14 2012 *)
Drop[CoefficientList[Series[x(13 -24x +16x^2 -4x^3)/(1-x)^4, {x, 0, 60}], x], 1] (* Vincenzo Librandi, Oct 17 2013 *)

PARI

vector(60, n, (n+2)*((n+2)^2+9*(n+2)-10)/6) \\ G. C. Greubel, Oct 30 2019

Sage

[n*(n^2+9*n-10)/6 for n in (0..60)] # G. C. Greubel, Oct 30 2019

Formula

a(n) = A023551(n+1) + 4.

From Colin Barker, Sep 17 2012: (Start)

a(n) = n*(n^2+9*n-10)/6.

G.f.: x^3*(13 - 24*x + 16*x^2 - 4*x^3)/(1-x)^4. (End)

E.g.f.: x^2*(-12 + (12+x)*exp(x))/6. - G. C. Greubel, Oct 30 2019

Extensions

Closed-form formula corrected by Colin Barker, Sep 17 2012