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

Author

Michael Somos, Jul 07 2014

Keywords

• sign
• easy

Comments

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

Examples

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

Links

• 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).

Crossrefs

Cf. A011558, A080891, A100047.

Programs

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 *)

PARI

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

PARI

{a(n) = sign( centerlift( Mod(n, 5)))};

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