A238469 Period 7: repeat [0, 1, 0, 0, 0, 0, -1].

0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1

Offset

0

Comments

This sequence is called B(n) in a comment on A234044 where it appears, together with five others, in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details, also for the n = 4 example.

Links

Table of n, a(n) for n=0..90.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,-1,-1).

Formula

G.f.: x*(1 - x^5)/(1 - x^7).

a(n+7) = a(n), n >= 0, a(k) = 0 for k = 0, 2, 3, 4, 5 and a(1) = -a(6) = 1.

a(n) = (n+1)^6 mod 7 - (n+6)^6 mod 7. - Paolo P. Lava, Feb 28 2014

From Wesley Ivan Hurt, Jul 18 2016: (Start)

a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) = 0 for n>5.

a(n) = floor(n/7) - floor((1+n)/7) - floor((5+n)/7) + floor((6+n)/7). (End)

Maple

P:=proc(q) local n;
for n from 0 to q do print(((n+1)^6 mod 7)-((n+6)^6 mod 7));
od; end: P(100); # Paolo P. Lava, Feb 28 2014
seq(op([0, 1, 0, 0, 0, 0, -1]), n=0..20); # Wesley Ivan Hurt, Jul 18 2016

Mathematica

PadRight[{}, 100, {0, 1, 0, 0, 0, 0, -1}] (* Wesley Ivan Hurt, Jul 18 2016 *)

Prog

(PARI) a(n)=(n+1)^6%7 - (n+6)^6%7 \\ Charles R Greathouse IV, Jul 17 2016
(Magma) &cat [[0, 1, 0, 0, 0, 0, -1]^^20]; // Wesley Ivan Hurt, Jul 18 2016

Crossrefs

Cf. A234044, A234045, A234046, A238468, A238470.

Sequence in context: A030213 A187969 A132151 * A288596 A284745 A103588

Adjacent sequences: A238466 A238467 A238468 * A238470 A238471 A238472

Keyword

sign,easy

Author

Wolfdieter Lang, Feb 27 2014

Status

approved