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A000044
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Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n >= 13, a(n) = a(n-1)+a(n-2)-a(n-13).
(Formerly M0691 N0255)
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4
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1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 232, 375, 606, 979, 1582, 2556, 4130, 6673, 10782, 17421, 28148, 45480, 73484, 118732, 191841, 309967, 500829, 809214, 1307487, 2112571, 3413385, 5515174, 8911138, 14398164, 23263822, 37588502, 60733592, 98130253, 158553878, 256183302, 413927966, 668803781, 1080619176, 1746009572, 2821113574, 4558212008
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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.
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,1,0,1,0,1,0,1,0,1).
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FORMULA
| G.f.: 1/(1 - z - z^3 - z^5 - z^7 - z^9 -z^11)
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MAPLE
| 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;
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MATHEMATICA
| CoefficientList[Series[1/(1 - z - z^3 - z^5 - z^7 - z^9 - z^11), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 10 2011. *)
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PROG
| (MAGMA) [ n eq 1 select 1 else n le 13 select Fibonacci(n-1) else Self(n-1)+Self(n-2)-Self(n-13): n in [1..50] ]; // Klaus Brockhaus, Dec 21 2010
(PARI) Vec(1/(1-z-z^3-z^5-z^7-z^9-z^11)+O(z^50)) \\ Charles R Greathouse IV, Jun 10 2011
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CROSSREFS
| Cf. A107358. See A000045 for the Fibonacci numbers.
Sequence in context: A189722 A023441 A023442 * A107358 A185357 A132636
Adjacent sequences: A000041 A000042 A000043 * A000045 A000046 A000047
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com); entry revised May 25 2005
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EXTENSIONS
| G.f. corrected by Charles R Greathouse IV, Jun 10 2011
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