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A160333 Number of pairs of rabbits in month n in the dying rabbits problem, if they become mature after 4 months and give birth to exactly 7 pairs, one per month. 1
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; text; internal format)
OFFSET
0,5
COMMENTS
The dying rabbits problem of immortal rabbits and matureness after 1 month defines the Fibonacci sequence.
For 0 <= n <= 9, a(n) = A003269(n+1), but a(10) = A003269(11) - 1 because of the death of the first pair of rabbits. - Robert FERREOL, Oct 05 2017
LINKS
Antonio M. Oller-Marcén, The Dying Rabbit Problem Revisited, INTEGERS 9 (2009), 129-138
FORMULA
G.f.: -(1 + x + x^2 + x^3 + x^4)*(x^4 - x^3 + x^2 - x + 1)/(-1 + x - x^2 + x^3 + x^5 + x^7 + x^9). - R. J. Mathar, May 12 2009
G.f.: (1 - x^10) / (1 - x - x^4 + x^11) = 1 / (1 - x / (1 - x^3 / (1 + x^3 / (1 - x^3 / (1 + x^3 / (1 - x / (1 + x / (1 - x / (1 + x))))))))). - Michael Somos, Jan 03 2013
a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-5) + a(n-7) + a(n-9). - Joerg Arndt, Oct 04 2017
a(n)=1 for 0 <= n <= 3, a(n) = a(n-1) + a(n-4) for 4 <= n <= 9, and a(n) = a(n-4) + a(n-5) + ... + a(n-10) for n >= 10. - Robert FERREOL, Oct 04 2017
EXAMPLE
The number of pairs at the 13th month is 32.
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
MATHEMATICA
LinearRecurrence[{1, -1, 1, 0, 1, 0, 1, 0, 1}, {1, 1, 1, 1, 2, 3, 4, 5, 7}, 50] (* Harvey P. Dale, Apr 23 2011 *)
PROG
(PARI) {a(n) = if( n<0, n = -n; polcoeff( (x^6 - x^10) / (1 - x^7 - x^10 + x^11) + x * O(x^n), n), polcoeff( (1 - x^10) / (1 - x - x^4 + x^11) + x * O(x^n), n))} /* Michael Somos, Jan 03 2013 */
CROSSREFS
Sequence in context: A006950 A052335 A193771 * A174578 A241733 A241338
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, May 09 2009
EXTENSIONS
Edited and extended by R. J. Mathar, May 12 2009
Name corrected by Robert FERREOL, Nov 18 2017
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)