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A107358
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Dying rabbits: a(n) = Fibonacci(n) for n <= 12; for n >= 13, a(n)=a(n-1)+a(n-2)-a(n-13).
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2
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0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 376, 608, 982, 1587, 2564, 4143, 6694, 10816, 17476, 28237, 45624, 73717, 119108, 192449, 310949, 502416, 811778, 1311630, 2119265, 3424201, 5532650, 8939375, 14443788, 23337539, 37707610, 60926041, 98441202, 159056294
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| In the limit, the growth rate is 1.61575... per generation as opposed to 1.61803... for Fibonacci numbers. - T. D. Noe, Jan 22 2009
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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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
Index to sequences with linear recurrences with constant coefficients, signature (1,1,0,0,0,0,0,0,0,0,0,0,-1).
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FORMULA
| G.f.: x/((x-1)*(1+x)*(x^11+x^9+x^7+x^5+x^3+x-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 27 2009]
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MAPLE
| with(combinat); f:=proc(n) option remember; if n <= 12 then RETURN(fibonacci(n)); fi; f(n-1)+f(n-2)-f(n-13); end;
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PROG
| (PARI) Vec(x/(x^13-x^2-x+1)+O(x^99)) \\ Charles R Greathouse IV, Jun 10 2011
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CROSSREFS
| See A000045 for the Fibonacci numbers. This is a better version of A000044.
Sequence in context: A023441 A023442 A000044 * A185357 A132636 A152163
Adjacent sequences: A107355 A107356 A107357 * A107359 A107360 A107361
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 25 2005
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