OFFSET
0,5
COMMENTS
Convolution inverse of A164118.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1).
FORMULA
Euler transform of length 10 sequence [-1, 1, 0, 1, 1, 0, 0, 0, 0, -1].
a(n) = -b(n) where b(n) is multiplicative with b(2) = -1, b(2^e) = -2 if e>1, b(p^e) = 1 if p>2.
a(n) = a(-n) for all n in Z. a(n+4) = a(n) unless n=0 or n=-4.
G.f.: (1 - x + x^2 - x^3 + x^4) / (1 - x^4).
a(n) = (-1)^n * A164415(n).
EXAMPLE
G.f. = 1 - x + x^2 - x^3 + 2*x^4 - x^5 + x^6 - x^7 + 2*x^8 - x^9 + x^10 + ...
MATHEMATICA
CoefficientList[Series[(1-x)(1-x^10)/((1-x^2)(1-x^4)(1-x^5)), {x, 0, 120}], x] (* Harvey P. Dale, Nov 28 2014 *)
PROG
(PARI) {a(n) = (-1)^n - (n==0) + (n%4==0)};
(PARI) {a(n) = -(n==0) + [2, -1, 1, -1][n%4 + 1]};
(Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)*(1-x^10)/((1-x^2)*(1-x^4)*(1-x^5)))); // G. C. Greubel, Sep 25 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Michael Somos, Aug 10 2009
STATUS
approved