|
%I #22 Apr 16 2024 21:20:11
%S 1,14,60,360,1904,10528,57280,313472,1711872,9355776,51117056,
%T 279316480,1526198272,8339333120,45566902272,248982306816,
%U 1360464379904,7433716105216,40618579197952,221944046157824,1212724817166336,6626451640025088,36207605093236736
%N 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.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 16, 16).
%F G.f.: -x*(1+12*x+16*x^2) / ( (2*x+1)*(8*x^2+4*x-1) ). - _Harvey P. Dale_, May 03 2011
%F a(n) = (A180222(n+2) +(-2)^n)/2. - _R. J. Mathar_, Oct 08 2016
%e a(5) = 1904 = 2*a(4) + 16*a(3) + 16*a(2) = 2*360 + 16*60 + 16*14.
%e a(4) = 360 since term (1,1) of X^4 = 360.
%t 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 *)
%Y Cf. A180222.
%K nonn,easy,changed
%O 1,2
%A _Gary W. Adamson_, May 11 2008
|
