A162265 a(n) = (2*n^3 + 5*n^2 - 5*n)/2.

1, 13, 42, 94, 175, 291, 448, 652, 909, 1225, 1606, 2058, 2587, 3199, 3900, 4696, 5593, 6597, 7714, 8950, 10311, 11803, 13432, 15204, 17125, 19201, 21438, 23842, 26419, 29175, 32116, 35248, 38577, 42109, 45850, 49806, 53983, 58387, 63024, 67900

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. A154684.

Programs

Magma

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

Maple

A162265:=n->(2*n^3 + 5*n^2 - 5*n)/2: seq(A162265(n), n=1..60); # Wesley Ivan Hurt, Apr 11 2017

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {4, 19, 51, 106}, 50] (* or *) CoefficientList[Series[(1+9*x-4*x^2)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Mar 05 2012 *)
Table[(2n^3+5n^2-5n)/2,{n,40}] (* Harvey P. Dale, May 25 2023 *)

PARI

5*binomial(n,2)+n^3 \\ Charles R Greathouse IV, Jan 11 2012

Formula

Row sums from A154684: a(n) = Sum_{m=1..n} 2*m*n+m+n-3.

G.f.: x*(1+9*x-4*x^2)/(1-x)^4. - Vincenzo Librandi, Mar 05 2012

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Mar 05 2012