OFFSET
0,1
COMMENTS
If p is prime, p divides a(p).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,1).
FORMULA
a(n) = a(n-5) + a(n-6) with a(0)=6, a(1)=a(2)=a(3)=a(4)=0, a(5)=5.
a(n) = Sum_{i=1..6} (x_i)^n where x_i are the roots of x^6 = x+1.
G.f.: (x^5-6) / (x^6+x^5-1). - Colin Barker, Jun 16 2013
a(0) = 6 and a(n) = n*Sum_{k=1..floor(n/5)} binomial(k,n-5*k)/k for n > 0. - Seiichi Manyama, Mar 04 2019
From Aleksander Bosek, Mar 06 2019: (Start)
a((s+6)*n+m) = Sum_{l=0..n} binomial(n-l,l)*a(s*n+l+m) for all s > 0, m > 0.
a(m) = Sum_{l=0..n}(-1)^{n-l} binomial(n-l,l)*a(m+n+5*l)for all m > 0. (End)
MAPLE
a:=n->n*add(binomial(k, n-5*k)/k, k=1..floor(n/5)): 6, seq(a(n), n=1..65); # Muniru A Asiru, Mar 09 2019
PROG
(GAP) Concatenation([6], List([1..65], n->n*Sum([1..Int(n/5)], k->Binomial(k, n-5*k)/k))); # Muniru A Asiru, Mar 09 2019
(PARI) polsym(x^6-x-1, 66) \\ Joerg Arndt, Mar 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Oct 27 2003
STATUS
approved