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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

G. C. Greubel, Table of n, a(n) for n = 0..1000

Antonio M. Oller-Marcén, The Dying Rabbit Problem Revisited, INTEGERS 9 (2009), 129-138

Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, 0, 1, 0, 1, 0, 1).

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

Cf. A000045, A000930.

Sequence in context: A006950 A052335 A193771 * A174578 A241733 A241338

Adjacent sequences:  A160330 A160331 A160332 * A160334 A160335 A160336

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 February 21 22:10 EST 2020. Contains 332113 sequences. (Running on oeis4.)