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%I #26 Oct 17 2017 08:37:21
%S 1,1,1,2,3,5,7,11,17,26,40,61,94,144,221,339,520,798,1224,1878,2881,
%T 4420,6781,10403,15960,24485,37564,57629,88412,135638,208090,319243,
%U 489769,751383,1152740,1768485,2713135,4162377,6385743,9796737
%N A Fibonacci-like model in which each pair of rabbits dies after the birth of their 4th litter: a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5).
%C Lim_{n->infinity} a(n+1)/a(n) = 1.534157744914.... is the root of x^5 = x^3 + x^2 + x + 1. - _Benoit Cloitre_, Jun 22 2002
%C A pair of rabbits born in month n begins to procreate in month n + 2, continues to procreate until month n + 5, and dies at the end of this month (each pair therefore gives birth to 5-2+1 = 4 pairs); the first pair is born in month 1. - _Robert FERREOL_, Oct 05 2017
%H N. T. Gridgeman, <a href="http://www.fq.math.ca/Scanned/11-1/gridgeman.pdf">A New Look at Fibonacci Generalization</a>, Fibonacci Quart., vol. 11 (1973), no. 1, 40-55.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,1).
%F a(n) = a(n-1) + a(n-2) - a(n-6);
%F G.f.: = (1 + x)/(1 - x^2 - x^3 - x^4 - x^5).
%F a(n) = A013982(n) + A013982(n-1). - _R. J. Mathar_, Nov 29 2011
%p a:=proc(n,p,q) option remember:
%p if n<=p then 1
%p elif n<=q then a(n-1,p,q)+a(n-p,p,q)
%p else add(a(n-k,p,q),k=p..q) fi end:
%p seq(a(n,2,5),n=0..100); # _Robert FERREOL_, Oct 05 2017
%t CoefficientList[ Series[(1 + x)/(1 - x^2 - x^3 - x^4 - x^5), {x, 0, 40}], x]
%t LinearRecurrence[{0,1,1,1,1},{1,1,1,2,3},40] (* _Harvey P. Dale_, Sep 01 2014 *)
%o (PARI) x='x+O('x^99); Vec((1+x)/(1-x^2-x^3-x^4-x^5)) \\ _Altug Alkan_, Oct 06 2017
%Y Cf. A013982.
%K easy,nonn
%O 0,4
%A Leonardo Fonseca (fonleo(AT)fisica.ufmg.br), Jun 19 2002
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