|
%I #20 Jun 13 2015 00:48:57
%S 0,1,1,2,3,5,8,12,19,29,45,69,106,163,250,384,589,904,1387,2128,3265,
%T 5009,7685,11790,18088,27750,42573,65314,100202,153726,235840,361816,
%U 555083,851585,1306466,2004325,3074951
%N Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-6).
%C Diagonal sums of the Riordan array (1/(1-x),x(1+x+x^2+x^3)) yield a(n+1). - _Paul Barry_, May 10 2005
%H Robert Israel, <a href="/A023436/b023436.txt">Table of n, a(n) for n = 0..4837</a>
%H J. H. E. Cohn, <a href="http://www.fq.math.ca/Scanned/2-2/cohn1.pdf">Letter to the editor</a>, Fib. Quart. 2 (1964), 108.
%H V. E. Hoggatt, Jr. and D. A. Lind, <a href="http://www.fq.math.ca/Scanned/7-5/hoggatt.pdf">The dying rabbit problem</a>, Fib. Quart. 7 (1969), 482-487.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,0,-1).
%F G.f.: x/(1 - x - x^2 + x^6) = x/((1 - x)(1 - x^2 - x^3 - x^4 - x^5)). - _Paul Barry_, May 10 2005
%p f:= gfun:-rectoproc({a(n)=a(n-1) + a(n-2) - a(n-6), seq(a(i)=0,i=-4..0),a(1)=1},a(n),'remember'):
%p seq(f(n),n=0..50); # _Robert Israel_, Dec 29 2014
%t a=b=c=d=e=0;f=1;lst={e,f};Do[g=e+f-a;AppendTo[lst,g];a=b;b=c;c=d;d=e;e=f;f=g,{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 30 2009 *)
%t LinearRecurrence[{1,1,0,0,0,-1},{0,1,1,2,3,5},40] (* _Harvey P. Dale_, Dec 21 2014 *)
%K nonn
%O 0,4
%A _N. J. A. Sloane_
|
