A162261 a(n) = (2*n^3 + 5*n^2 - 7*n)/2.

0, 11, 39, 90, 170, 285, 441, 644, 900, 1215, 1595, 2046, 2574, 3185, 3885, 4680, 5576, 6579, 7695, 8930, 10290, 11781, 13409, 15180, 17100, 19175, 21411, 23814, 26390, 29145, 32085, 35216, 38544, 42075, 45815, 49770, 53946, 58349, 62985, 67860

Offset: 1

Author

Vincenzo Librandi, Jun 29 2009

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A151675, A155724.

Programs

Magma

[(2*n^3 + 5*n^2 - 7*n)/2 : n in [1..50]]; // Wesley Ivan Hurt, May 07 2021

Mathematica

CoefficientList[Series[x*(11-5*x)/(1-x)^4,{x,0,40}],x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 11, 39, 90}, 50](* Vincenzo Librandi, Mar 04 2012 *)

Python

def A162261(n): return n*(2*pow(n,2) +5*n -7)//2
print([A162261(n) for n in range(1,61)]) # G. C. Greubel, Jan 21 2025

Formula

Row sums from A155724: a(n) = Sum_{m=1..n} (2*m*n + m + n - 4).

From Vincenzo Librandi, Mar 04 2012: (Start)

G.f.: x^2*(11 - 5*x)/(1-x)^4.

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

a(n) = A151675(n) - 8*n. - L. Edson Jeffery, Oct 12 2012

From Amiram Eldar, Feb 25 2023: (Start)

Sum_{n>=2} 1/a(n) = 8*log(2)/63 + 1166/19845.

Sum_{n>=2} (-1)^n/a(n) = (32*log(2) - 2*Pi - 3566/315)/63. (End)

E.g.f.: (1/2)*x^2*(11 + 2*x)*exp(x). - G. C. Greubel, Jan 21 2025

Extensions

New name from Vincenzo Librandi, Mar 04 2012