A330025 a(n) = (-1)^floor(n/5) * sign(mod(n, 5)).

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, Nov 27 2019

Keywords

• sign
• easy

Comments

This is a strong elliptic divisibility sequence t_n as given in [Kimberling, p. 16] where x = 1, y = 1, z = 1. - Michael Somos, Mar 17 2020

Examples

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

Links

• Clark 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, A099443, A163812, A332828.

Programs

Mathematica

a[ n_] := (-1)^Quotient[n, 5] Sign@Mod[n, 5];

PARI

{a(n) = (-1)^(n\5) * sign(n%5)};

Formula

Euler transform of length 10 sequence [1, 0, 0, -1, -1, 0, 0, 0, 0, 1].

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

a(n) = A099443(n-1). a(n) = A163812(n) except n=0.

a(n) = (-1)^floor(n/5) * A011558(n) for all n in Z.

0 = a(n)*a(n+4) - a(n+1)*a(n+3) + a(n+2)^2 = a(n)*a(n+5) - a(n+1)*a(n+4) + a(n+2)*a(n+3) for all n in Z. - Michael Somos, Mar 17 2020