Search: id:A000044
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%I A000044 M0691 N0255
%S A000044 1,1,1,2,3,5,8,13,21,34,55,89,144,232,375,606,979,1582,2556,4130,6673,
               10782,
%T A000044 17421,28148,45480,73484,118732,191841,309967,500829,809214,1307487,2112571,
%U A000044 3413385,5515174,8911138,14398164,23263822,37588502,60733592,98130253,
               158553878,256183302,413927966,668803781,1080619176,1746009572,2821113574,
               4558212008
%N A000044 Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n 
               >= 13, for n >= 13, a(n)=a(n-1)+a(n-2)-a(n-13).
%C A000044 A107358 is a more satisfactory version, but I have left the present sequence 
               unchanged (except for making the definition clearer) since it has 
               been in the OEIS so long.
%D A000044 J. H. E. Cohn, Letter to the editor, Fib. Quart. 2 (1964), 108.
%D A000044 V. E. Hoggatt, Jr. and D. A. Lind, The dying rabbit problem, Fib. Quart. 
               7 (1969), 482-487.
%D A000044 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000044 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%F A000044 G.f.: (1+z^2+z^4+z^6+z^8+z^10)/(1-z-z^3-z^5-z^7-z^9-z^11) . (Simon Plouffe:1031 
               Generating Functions) Note:for 1 to 9 numbers:0,1,1,2,3,5,8,13,21 
               . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 17 2009]
%p A000044 with(combinat); f:=proc(n) option remember; if n=0 then RETURN(1); fi; 
               if n <= 12 then RETURN(fibonacci(n)); fi; f(n-1)+f(n-2)-f(n-13); 
               end;
%p A000044 g:=(1+z^2+z^4+z^6+z^8+z^10)/(1-z-z^3-z^5-z^7-z^9-z^11): gser:=series(g, 
               z=0, 49): seq((coeff(gser, z, n)), n=-1..47);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 17 2009]
%Y A000044 Cf. A107358. See A000045 for the Fibonacci numbers.
%Y A000044 Sequence in context: A105471 A023441 A023442 this_sequence A107358 A132636 
               A152163
%Y A000044 Adjacent sequences: A000041 A000042 A000043 this_sequence A000045 A000046 
               A000047
%K A000044 nonn
%O A000044 0,4
%A A000044 N. J. A. Sloane (njas(AT)research.att.com); entry revised May 25 2005

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