A140184 a(n) = 2*a(n-1) + 16*a(n-2) + 16*a(n-3) for n>3 with a(1)=1, a(2)=14, a(3)=60.

1, 14, 60, 360, 1904, 10528, 57280, 313472, 1711872, 9355776, 51117056, 279316480, 1526198272, 8339333120, 45566902272, 248982306816, 1360464379904, 7433716105216, 40618579197952, 221944046157824, 1212724817166336, 6626451640025088, 36207605093236736

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (2, 16, 16).

Formula

G.f.: -x*(1+12*x+16*x^2) / ( (2*x+1)*(8*x^2+4*x-1) ). - Harvey P. Dale, May 03 2011

a(n) = (A180222(n+2) +(-2)^n)/2. - R. J. Mathar, Oct 08 2016

Example

a(5) = 1904 = 2*a(4) + 16*a(3) + 16*a(2) = 2*360 + 16*60 + 16*14.
a(4) = 360 since term (1,1) of X^4 = 360.

Mathematica

LinearRecurrence[{2, 16, 16}, {1, 14, 60}, 40] (* or *) CoefficientList[Series[(-1-12 x-16 x^2)/(-1+2 x+16 x^2+16 x^3), {x, 0, 40}], x] (* Harvey P. Dale, May 03 2011 *)

Crossrefs

Cf. A180222.

Sequence in context: A063492 A051799 A164540 * A264854 A189948 A252255

Adjacent sequences: A140181 A140182 A140183 * A140185 A140186 A140187

Keyword

nonn,easy

Author

Gary W. Adamson, May 11 2008

Status

approved