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A087936 Perrin sequence of order 6. 4
6, 0, 0, 0, 0, 5, 6, 0, 0, 0, 5, 11, 6, 0, 0, 5, 16, 17, 6, 0, 5, 21, 33, 23, 6, 5, 26, 54, 56, 29, 11, 31, 80, 110, 85, 40, 42, 111, 190, 195, 125, 82, 153, 301, 385, 320, 207, 235, 454, 686, 705, 527, 442, 689, 1140, 1391, 1232, 969, 1131, 1829, 2531, 2623, 2201, 2100 (list; graph; refs; listen; history; text; internal format)
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

Column 5 of A306646.

Cf. A001608, A050443.

Cf. A087935.

Sequence in context: A228632 A229657 A306550 * A089804 A270606 A087255

Adjacent sequences:  A087933 A087934 A087935 * A087937 A087938 A087939

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Oct 27 2003

STATUS

approved

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)