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A226591 A single pair of rabbits (male and female) is born at the beginning of a year. Assume the following conditions: 1. Rabbits are able to mate at the age of 2 months. 2. Rabbit pairs are not fertile during their first 5 months of life, but thereafter give birth to 1 new male/female pairs at the end of every 3 month. 3. Rabbits will die after 12 months from birth. 0
1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 4, 6, 6, 7, 10, 9, 12, 14, 14, 20, 20, 23, 30, 29, 39, 44, 46, 62, 63, 76, 94, 95, 124, 137, 151, 195, 202, 246, 293, 309, 395, 433, 492, 612, 648, 792, 921, 1003, 1253, 1374, 1593, 1928, 2084, 2537, 2907, 3244, 3973, 4379, 5133, 6088, 6702, 8103, 9214, 10461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..66.

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

EXAMPLE

For 1<=n<=5, a(n)=1. For 6<=n<=12, a(n)=a(n-3)+a(n-5). For n>=13, a(n) = a(n-5) + a(n-8) + a(n-11).

G.f.: (x*(1+x)*(1-x+x^2)*(1+x+x^2)*(1-x^2+x^4))/(1-x^2+x^4-x^5-x^6+x^7-x^9); a(n) = +1*a(n-2) -1*a(n-4) +1*a(n-5) +1*a(n-6) -1*a(n-7) +1*a(n-9). [Joerg Arndt, Jul 06 2013]

MATHEMATICA

Join[{1}, LinearRecurrence[{0, 1, 0, -1, 1, 1, -1, 0, 1}, {1, 1, 1, 1, 2, 2, 2, 3, 3}, 65]] (* Ray Chandler, Jul 15 2015 *)

PROG

(PARI) v=[1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5]; for(n=13, 100, v=concat(v, v[#v-4]+v[#v-7]+v[#v-10])); v \\ Charles R Greathouse IV, Jul 05 2013

CROSSREFS

Cf. A226592.

Sequence in context: A163001 A239913 A323701 * A194223 A194251 A029114

Adjacent sequences:  A226588 A226589 A226590 * A226592 A226593 A226594

KEYWORD

nonn,easy

AUTHOR

Emily Lu, Jun 13 2013

STATUS

approved

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Last modified June 18 23:16 EDT 2021. Contains 345125 sequences. (Running on oeis4.)