A167191 a(n) = 4*n*(1 + 45*n + 620*n^2).

2664, 20568, 68592, 161616, 314520, 542184, 859488, 1281312, 1822536, 2498040, 3322704, 4311408, 5479032, 6840456, 8410560, 10204224, 12236328, 14521752, 17075376, 19912080, 23046744, 26494248, 30269472, 34387296, 38862600, 43710264, 48945168, 54582192, 60636216

Offset: 1

Author

A.K. Devaraj, Oct 30 2009

Keywords

• nonn
• easy

Comments

See A167190, where this sequence arises as the integer part of the quotient.

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. A167190.

Programs

Magma

I:=[2664, 20568, 68592, 161616]; [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..40]]; // Vincenzo Librandi, Jul 02 2012

Mathematica

CoefficientList[Series[24*(111+413*x+96*x^2)/(x-1)^4,{x,0,40}],x] (* Vincenzo Librandi, Jul 02 2012 *)
LinearRecurrence[{4,-6,4,-1},{2664,20568,68592,161616},40] (* Harvey P. Dale, Jun 15 2014 *)

Formula

G.f.: 24*x*(111+413*x+96*x^2)/(x-1)^4. - R. J. Mathar, Jan 27 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jul 02 2012

E.g.f.: 4*x*(666 + 1905*x + 620*x^2)*exp(x). - Elmo R. Oliveira, Aug 07 2025

Extensions

Extended beyond a(6) by R. J. Mathar, Nov 17 2009