|
%I #22 Jun 13 2015 00:52:10
%S 1,1,4,0,32,-64,384,-1280,5632,-21504,88064,-348160,1400832,-5586944,
%T 22380544,-89456640,357957632,-1431568384,5726797824,-22906142720,
%U 91626668032,-366502477824,1466018299904,-5864056422400,23456259244032,-93824969867264,375300013686784
%N a(1)=1, a(2)=1, a(3)=4, a(4)=0; a(n)=12a(n-2)-16a(n-3) for n>=5.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (-2,8).
%F G.f.: (-2*x^3 + 3*x^2 + x)/((1-2x) * (1+4x)). - _Ralf Stephan_, Jul 14 2013
%F a(n) = (16*2^n - (-4)^n)/48, n>0. - _Ralf Stephan_, Jul 18 2013
%p a[1]:=1: a[2]:=1: a[3]:=4: a[4]:=0: for n from 5 to 27 do a[n]:=12*a[n-2]-16*a[n-3] od: seq(a[n],n=1..27);
%t M = {{1, -1, -1, 1}, {-1, 1, -1, 1}, {-1, -1, 1, 1}, {1, 1, 1, -3}}; v[1] = {1, 0, 0, 0}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
%t LinearRecurrence[{-2,8},{1,1,4},30] (* _Harvey P. Dale_, Apr 23 2015 *)
%K sign,easy
%O 1,3
%A _Roger L. Bagula_, Sep 23 2006
%E Edited by _N. J. A. Sloane_, Oct 08 2006
|
