A023436 Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-6).

0, 1, 1, 2, 3, 5, 8, 12, 19, 29, 45, 69, 106, 163, 250, 384, 589, 904, 1387, 2128, 3265, 5009, 7685, 11790, 18088, 27750, 42573, 65314, 100202, 153726, 235840, 361816, 555083, 851585, 1306466, 2004325, 3074951

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 0..4837
• J. H. E. Cohn, Letter to the editor, Fib. Quart. 2 (1964), 108.
• V. E. Hoggatt, Jr. and D. A. Lind, The dying rabbit problem, Fib. Quart. 7 (1969), 482-487.
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,-1).

Programs

Maple

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'):
seq(f(n),n=0..50); # Robert Israel, Dec 29 2014

Mathematica

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 *)
LinearRecurrence[{1,1,0,0,0,-1},{0,1,1,2,3,5},40] (* Harvey P. Dale, Dec 21 2014 *)

Formula

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