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).

1, 1, 1, 2, 3, 5, 7, 11, 17, 26, 40, 61, 94, 144, 221, 339, 520, 798, 1224, 1878, 2881, 4420, 6781, 10403, 15960, 24485, 37564, 57629, 88412, 135638, 208090, 319243, 489769, 751383, 1152740, 1768485, 2713135, 4162377, 6385743, 9796737

Offset: 0

Author

Leonardo Fonseca (fonleo(AT)fisica.ufmg.br), Jun 19 2002

Keywords

• easy
• nonn

Comments

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

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

Links

• N. T. Gridgeman, A New Look at Fibonacci Generalization, Fibonacci Quart., vol. 11 (1973), no. 1, 40-55.
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,1).

Crossrefs

Cf. A013982.

Programs

Maple

a:=proc(n,p,q) option remember:
if n<=p then 1
elif n<=q then a(n-1,p,q)+a(n-p,p,q)
else add(a(n-k,p,q),k=p..q) fi end:
seq(a(n,2,5),n=0..100); # Robert FERREOL, Oct 05 2017

Mathematica

CoefficientList[ Series[(1 + x)/(1 - x^2 - x^3 - x^4 - x^5), {x, 0, 40}], x]
LinearRecurrence[{0,1,1,1,1},{1,1,1,2,3},40] (* Harvey P. Dale, Sep 01 2014 *)

PARI

x='x+O('x^99); Vec((1+x)/(1-x^2-x^3-x^4-x^5)) \\ Altug Alkan, Oct 06 2017

Formula

a(n) = a(n-1) + a(n-2) - a(n-6);

G.f.: = (1 + x)/(1 - x^2 - x^3 - x^4 - x^5).

a(n) = A013982(n) + A013982(n-1). - R. J. Mathar, Nov 29 2011