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A160333
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Number of pairs of rabbits in month n in the dying rabbits problem, if they die after 7 months and become mature after 4 months.
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1
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1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 17, 23, 32, 44, 59, 79, 107, 146, 198, 267, 361, 490, 665, 900, 1217, 1648, 2234, 3027, 4098, 5548, 7515, 10181, 13789, 18672, 25287, 34251, 46392, 62830, 85090, 115243, 156087, 211402, 286311, 387765, 525180, 711295, 963355, 1304728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The dying rabbits problem of immortal rabbits and matureness after 1 month defines the Fibonacci sequence.
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REFERENCES
| Antonio M. Oller-Marc\'en, "The Dying Rabbit Problem Revisited", INTEGERS, 9 (2009), 129-138
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LINKS
| Antonio M. Oller-Marc\'en, The Dying Rabbit Problem Revisited, INTEGERS 9 (2009), 129-138
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FORMULA
| G.f.: -(1+x^2+x^3+x^4+x)*(x^4-x^3+x^2-x+1)/(-1+x-x^2+x^3+x^5+x^7+x^9) [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2009]
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EXAMPLE
| The number of pairs at the 13th month is 32.
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MAPLE
| Cnh := proc(n, h) option remember ; if n < 0 then 0 ; elif n < h then 1; else procname(n-1, h)+procname(n-h, h) ; fi; end:
C := proc(n, k, h) option remember ; local i; if n >= 0 and n < k+h-1 then Cnh(n, h); else add( procname(n-h-i, k, h), i=0..k-1) ; fi; end:
A160333 := proc(n) C(n, 7, 4) ; end: seq(A160333(n), n=0..80) ; # R. J. Mathar, May 12 2009
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MATHEMATICA
| LinearRecurrence[{1, -1, 1, 0, 1, 0, 1, 0, 1}, {1, 1, 1, 1, 2, 3, 4, 5, 7}, 50] (* From Harvey P. Dale, Apr 23 2011 *)
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CROSSREFS
| Cf. A000045, A000930
Sequence in context: A006950 A106507 A052335 * A174578 A136422 A018127
Adjacent sequences: A160330 A160331 A160332 * A160334 A160335 A160336
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KEYWORD
| nonn
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AUTHOR
| Parthasarathy Nambi (PachaNambi(AT)yahoo.com), May 09 2009
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EXTENSIONS
| Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2009
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