A163655 a(n) = n*(2*n^2 + 5*n + 13)/2.

0, 10, 31, 69, 130, 220, 345, 511, 724, 990, 1315, 1705, 2166, 2704, 3325, 4035, 4840, 5746, 6759, 7885, 9130, 10500, 12001, 13639, 15420, 17350, 19435, 21681, 24094, 26680, 29445, 32395, 35536, 38874, 42415, 46165, 50130, 54316, 58729, 63375

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. A163652.

Programs

Mathematica

CoefficientList[Series[x*(10-9*x+5*x^2)/(x-1)^4,{x,0,40}],x] (* Vincenzo Librandi, Mar 05 2012 *)
LinearRecurrence[{4,-6,4,-1}, {0,10,31,69}, 50] (* G. C. Greubel, Aug 01 2017 *)

PARI

x='x+O('x^50); concat([0], Vec(x*(10-9*x+5*x^2)/(x-1)^4)) \\ G. C. Greubel, Aug 01 2017

Formula

Row sums from A163652: a(n) = Sum_{m=1..n} (2*m*n + m + n + 6).

G.f.: x*(10 - 9*x + 5*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*(20 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 01 2017

Extensions

Edited by R. J. Mathar, Aug 05 2009