OFFSET
0,4
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).
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).
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 *)
PROG
(PARI) x='x+O('x^99); Vec((1+x)/(1-x^2-x^3-x^4-x^5)) \\ Altug Alkan, Oct 06 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leonardo Fonseca (fonleo(AT)fisica.ufmg.br), Jun 19 2002
STATUS
approved