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%I #33 Dec 11 2021 04:55:10
%S 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,
%T 93,114,136,159,195,229,273,331,388,468,560,661,799,948,1129,1359,
%U 1609,1928,2307,2738,3287,3916,4666,5594,6654,7953,9510,11320,13547,16164
%N Expansion of g.f. x*(1+x+x^2)/(1-x^3-x^5).
%C Previous name was: 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.
%H T. D. Noe, <a href="/A226503/b226503.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,1).
%F a(n) = a(n-3) + a(n-5), a(1) = a(2) = a(3) = a(4) = a(5) = 1.
%F G.f.: x*(1+x+x^2)/(1-x^3-x^5). - _Joerg Arndt_, Jun 12 2013
%e a(6) = a(3) + a(1) = 1 + 1 = 2;
%e a(11) = a(8) + a(6) = 2 + 2 = 4.
%t LinearRecurrence[{0, 0, 1, 0, 1}, {1, 1, 1, 1, 1}, 50] (* _T. D. Noe_, Jun 12 2013 *)
%o (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]^(n-1)*[1;1;1;1;1])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016
%K nonn,easy
%O 1,6
%A _Kung Fan Kai_, Jun 12 2013
%E New name using g.f. from _Joerg Arndt_, Dec 11 2021
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