A026060 a(n) = dot_product(n,n-1,...2,1)*(5,6,...,n,1,2,3,4).

45, 80, 126, 184, 255, 340, 440, 556, 689, 840, 1010, 1200, 1411, 1644, 1900, 2180, 2485, 2816, 3174, 3560, 3975, 4420, 4896, 5404, 5945, 6520, 7130, 7776, 8459, 9180, 9940, 10740, 11581, 12464, 13390, 14360, 15375, 16436, 17544, 18700, 19905, 21160, 22466, 23824, 25235, 26700, 28220

Offset: 5

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 5..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Column 4 of triangle A094415.

Programs

Magma

[n*(n^2+15*n-46)/6: n in [5..60]]; // Vincenzo Librandi, Nov 15 2011

Mathematica

Table[n (n^2+15n-46)/6,{n,5,60}] (* or *) LinearRecurrence[{4,-6,4,-1},{45,80,126,184},60] (* Harvey P. Dale, Nov 05 2011 *)
Table[Range[n,1,-1].Join[Range[5,n],{1,2,3,4}],{n,5,60}] (* Harvey P. Dale, Aug 10 2025 *)

Formula

a(n) = n*(n^2 + 15*n - 46)/6. - Ralf Stephan, Apr 30 2004

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(5)=45, a(6)=80, a(7)=126, a(8)=184. - Harvey P. Dale, Nov 05 2011

G.f.: x^5*(45 - 100*x + 76*x^2 - 20*x^3)/(1-x)^4. - Colin Barker, Sep 17 2012