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
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.
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
KEYWORD
sign,easy
AUTHOR
Michael Somos, Jul 07 2014
STATUS
approved