A244895 Period 5: repeat [0, 1, 1, -1, -1].

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

Offset

0,1

Comments

This is a strong elliptic divisibility sequence t_n as given in [Kimberling, p. 16] where x = 1, y = z = -1.

Links

Table of n, a(n) for n=0..76.

C. Kimberling, Strong divisibility sequences and some conjectures, Fib. Quart., 17 (1979), 13-17.

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

Formula

G.f.: x * (1 + x) * (1 - x^2) / (1 - x^5).

Euler transform of length 5 sequence [ 1, -2, 0, 0, 1].

a(n) = -a(-n) = a(n + 5) for all n in Z.

0 = (a(n) + a(n+2)) * (a(n) - a(n+1) + a(n+2)) for all n in Z.

0 = a(n)*a(n+4) - a(n+1)*a(n+3) - a(n+2)*a(n+2) for all n in Z.

0 = a(n)*a(n+5) + a(n+1)*a(n+4) - a(n+2)*a(n+3) for all n in Z.

|A011558(n)| = |A080891(n)| = |A100047(n)| = |a(n)|. - Michael Somos, May 24 2015

a(5*n) = 0, a(5*n + 1) = a(5*n + 2) = 1, a(5*n + 3) = a(5*n + 4) = -1 for all n in Z. -Michael Somos, Nov 27 2019

Example

G.f. = x + x^2 - x^3 - x^4 + x^6 + x^7 - x^8 - x^9 + x^11 + x^12 + ...

Mathematica

a[ n_] := {1, 1, -1, -1, 0}[[Mod[ n, 5, 1]]]; (* Michael Somos, Jan 08 2015 *)
a[ n_] := Sign[ Mod[ n, 5, -2]]; (* Michael Somos, Jan 08 2015 *)
PadRight[{}, 120, {0, 1, 1, -1, -1}] (* Harvey P. Dale, Nov 11 2020 *)

Prog

(PARI) {a(n) = [0, 1, 1, -1, -1][n%5 + 1]};
(PARI) {a(n) = sign( centerlift( Mod(n, 5)))};

Crossrefs

Cf. A011558, A080891, A100047.

Sequence in context: A284944 A284674 A225181 * A330025 A330033 A332828

Adjacent sequences: A244892 A244893 A244894 * A244896 A244897 A244898

Keyword

sign,easy

Author

Michael Somos, Jul 07 2014

Status

approved