A163661 a(n) = n*(2*n^2 + 5*n + 17)/2.

0, 12, 35, 75, 138, 230, 357, 525, 740, 1008, 1335, 1727, 2190, 2730, 3353, 4065, 4872, 5780, 6795, 7923, 9170, 10542, 12045, 13685, 15468, 17400, 19487, 21735, 24150, 26738, 29505, 32457, 35600, 38940, 42483, 46235, 50202, 54390, 58805, 63453

Offset: 0

Author

Vincenzo Librandi, Aug 02 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A163657.

Programs

Mathematica

CoefficientList[Series[x*(12-13*x+7*x^2)/(x-1)^4,{x,0,40}],x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 12, 35, 75}, 50](* Vincenzo Librandi, Mar 06 2012 *)

PARI

x='x+O('x^50); concat([0], Vec(x*(12-13*x+7*x^2)/(x-1)^4)) \\ G. C. Greubel, Aug 01 2017

Formula

Row sums from A163657: a(n) = Sum_{m=1..n} (2*m*n + m + n + 8).

a(n) = A163655(n) + 2*n.

G.f.: x*(12 - 13*x + 7*x^2)/(x-1)^4.

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

E.g.f.: (1/2)*x*(24 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 01 2017

Extensions

Edited and a(31) corrected by R. J. Mathar, Aug 05 2009