

A226503


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 two 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. No rabbits die.


3



1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 7, 8, 9, 12, 13, 16, 20, 22, 28, 33, 38, 48, 55, 66, 81, 93, 114, 136, 159, 195, 229, 273, 331, 388, 468, 560, 661, 799, 948, 1129, 1359, 1609, 1928, 2307, 2738, 3287, 3916, 4666, 5594, 6654, 7953, 9510, 11320, 13547, 16164
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OFFSET

1,6


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,1).


FORMULA

a(n) = a(n3) + a(n5), a(1) = a(2) = a(3) = a(4) = a(5) = 1.
G.f.: x*(1+x+x^2)/(1x^3x^5).  Joerg Arndt, Jun 12 2013


EXAMPLE

a(6)=a(3)+a(1)=1+1=2, a(11)=a(8)+a(6)=2+2=4.


MATHEMATICA

LinearRecurrence[{0, 0, 1, 0, 1}, {1, 1, 1, 1, 1}, 50] (* T. D. Noe, Jun 12 2013 *)


PROG

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, 0, 1, 0, 0]^(n1)*[1; 1; 1; 1; 1])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016


CROSSREFS

Sequence in context: A029057 A087897 A029056 * A036847 A282379 A029055
Adjacent sequences: A226500 A226501 A226502 * A226504 A226505 A226506


KEYWORD

nonn,easy


AUTHOR

Kung Fan Kai, Jun 12 2013


STATUS

approved



