A026037 a(n) = dot_product(1,2,...,n)*(3,4,...,n,1,2).

11, 22, 40, 67, 105, 156, 222, 305, 407, 530, 676, 847, 1045, 1272, 1530, 1821, 2147, 2510, 2912, 3355, 3841, 4372, 4950, 5577, 6255, 6986, 7772, 8615, 9517, 10480, 11506, 12597, 13755, 14982, 16280, 17651, 19097, 20620, 22222, 23905, 25671, 27522, 29460, 31487, 33605, 35816, 38122, 40525, 43027

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

Column 2 of triangle A094414.

Programs

Magma

I:=[11, 22, 40, 67]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 20 2012

Mathematica

s=0;lst={};Do[s+=n^2+2;If[s>10, AppendTo[lst, s]], {n, 0, 6!, 1}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)
Table[n (2n^2-3n+13)/6,{n,3,60}]  (* Harvey P. Dale, Apr 22 2011 *)
LinearRecurrence[{4,-6,4,-1},{11,22,40,67},50] (* Vincenzo Librandi, Jun 20 2012 *)

Formula

n(2n^2 - 3n + 13)/6. - Ralf Stephan, Apr 30 2004

G.f.: -x^3*(-11 + 22*x - 18*x^2 + 5*x^3) / (x - 1)^4 . - R. J. Mathar, Apr 17 2011

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 20 2012