OFFSET
0,3
COMMENTS
In his essay "La Cochonnerie ou calcul estimatif...", French military engineer Vauban (1633-1707) writes about this Fibonacci-like sequence for the year-by-year growth of pigs. - Charles R Greathouse IV, Sep 16 2015
REFERENCES
Sébastien Le Prestre de Vauban, La cochonnerie ou calcul estimatif pour connaître jusqu'où peut aller la production d'une truie pendant dix années de temps (1699).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Pierre de la Harpe, Vauban pour les cochons comme Fibonacci pour les lapins, Images des Mathématiques, CNRS, 2013.
Index entries for linear recurrences with constant coefficients, signature (3, 6, 6, 6, 6).
FORMULA
G.f.: x/(1-3*x-6*x^2-6*x^3-6*x^4-6*x^5). - Philippe Deléham, Apr 17 2013
MAPLE
f:=proc(n) option remember;
if n <= 0 then 0 elif n=1 then 1 else
3*f(n-1)+6*f(n-2)+6*f(n-3)+6*f(n-4)+6*f(n-5); fi; end;
[seq(f(n), n=0..30)];
MATHEMATICA
LinearRecurrence[{3, 6, 6, 6, 6}, {0, 1, 3, 15, 69}, 40] (* T. D. Noe, Apr 17 2013 *)
CoefficientList[Series[x/(1 - 3 x - 6 x^2 - 6 x^3 - 6 x^4 - 6 x^5), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 17 2015 *)
PROG
(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 6, 6, 6, 6, 3]^n*[0; 1; 3; 15; 69])[1, 1] \\ Charles R Greathouse IV, Sep 16 2015
(Magma) I:=[0, 1, 3, 15, 69]; [n le 5 select I[n] else 3*Self(n-1)+6*Self(n-2)+6*Self(n-3)+6*Self(n-4)+6*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Sep 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Pierre de la Harpe, Apr 17 2013
STATUS
approved