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Search: id:A000044
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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, for n >= 13, a(n)=a(n-1)+a(n-2)-a(n-13).
(Formerly M0691 N0255)
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+0
3
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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; listen)
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OFFSET
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0,4
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COMMENT
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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
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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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FORMULA
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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]
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MAPLE
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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;
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]
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CROSSREFS
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Cf. A107358. See A000045 for the Fibonacci numbers.
Adjacent sequences: A000041 A000042 A000043 this_sequence A000045 A000046 A000047
Sequence in context: A105471 A023441 A023442 this_sequence A107358 A132636 A152163
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com); entry revised May 25 2005
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