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

Author

Gary W. Adamson, May 11 2008

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

Cf. A180222.

Programs

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 *)

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