cp's OEIS Frontend

A072465 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).

%I A072465 #28 Jan 05 2025 19:51:37
%S A072465 1,1,1,2,3,5,7,11,17,26,40,61,94,144,221,339,520,798,1224,1878,2881,
%T A072465 4420,6781,10403,15960,24485,37564,57629,88412,135638,208090,319243,
%U A072465 489769,751383,1152740,1768485,2713135,4162377,6385743,9796737
%N A072465 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 A072465 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 A072465 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 A072465 N. T. Gridgeman, <a href="https://web.archive.org/web/2024*/https://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 A072465 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,1).
%F A072465 a(n) = a(n-1) + a(n-2) - a(n-6);
%F A072465 G.f.: = (1 + x)/(1 - x^2 - x^3 - x^4 - x^5).
%F A072465 a(n) = A013982(n) + A013982(n-1). - _R. J. Mathar_, Nov 29 2011
%p A072465 a:=proc(n,p,q) option remember:
%p A072465 if n<=p then 1
%p A072465 elif n<=q then a(n-1,p,q)+a(n-p,p,q)
%p A072465 else add(a(n-k,p,q),k=p..q) fi end:
%p A072465 seq(a(n,2,5),n=0..100); # _Robert FERREOL_, Oct 05 2017
%t A072465 CoefficientList[ Series[(1 + x)/(1 - x^2 - x^3 - x^4 - x^5), {x, 0, 40}], x]
%t A072465 LinearRecurrence[{0,1,1,1,1},{1,1,1,2,3},40] (* _Harvey P. Dale_, Sep 01 2014 *)
%o A072465 (PARI) x='x+O('x^99); Vec((1+x)/(1-x^2-x^3-x^4-x^5)) \\ _Altug Alkan_, Oct 06 2017
%Y A072465 Cf. A013982.
%K A072465 easy,nonn
%O A072465 0,4
%A A072465 Leonardo Fonseca (fonleo(AT)fisica.ufmg.br), Jun 19 2002