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 A226591 Expansion of 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). 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 COMMENTS 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 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. LINKS 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). From Joerg Arndt, Jul 06 2013: (Start) 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). (End) 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 EXTENSIONS New name using g.f. from Joerg Arndt, Dec 11 2021 STATUS approved

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Last modified July 6 18:12 EDT 2022. Contains 355114 sequences. (Running on oeis4.)