

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
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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(n3)+a(n5). For n>=13, a(n) = a(n5) + a(n8) + a(n11).
G.f.: (x*(1+x)*(1x+x^2)*(1+x+x^2)*(1x^2+x^4))/(1x^2+x^4x^5x^6+x^7x^9); a(n) = +1*a(n2) 1*a(n4) +1*a(n5) +1*a(n6) 1*a(n7) +1*a(n9). [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[#v4]+v[#v7]+v[#v10])); 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



