login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188578 Expansion of (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15) in powers of x. 0
1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

M. Somos, Rational Function Multiplicative Coefficients

FORMULA

Euler transform of length 15 sequence [ 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1].

a(n) = b(2*n + 1) where b(n) is multiplicative with b(p^e) = 0^e if p<7, b(p^e) = 1, if p == 1, 17, 19, 23 (mod 30), b(p^e) = (-1)^e if p == 7, 11, 13, 29 (mod 30).

G.f.: (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15). a(-1 - n) = -a(n).

G.f.: (1-x)^2 *(1+x) *(1+x+x^2) *(1-x+x^2) / (1-x+x^3-x^4+x^5-x^7+x^8). - R. J. Mathar, Apr 09 2011

a(n) = -a(-1-n) = a(n+15) for all n in Z. - Michael Somos, May 21 2015

a(2*n) = a(n-4), a(2*n + 1) = a(n+4), a(3*n) = A080891(n+1), a(3*n + 1) = 0, a(3*n + 2) = -A080891(n) for all n in Z. - Michael Somos, May 21 2015

EXAMPLE

G.f. = 1 - x^3 - x^5 - x^6 + x^8 + x^9 + x^11 - x^14 + x^15 - x^18 - x^20 + ...

G.f. = q - q^7 - q^11 - q^13 + q^17 + q^19 + q^23 - q^29 + q^31 - q^37 - q^41 + ...

MATHEMATICA

a[ n_] := KroneckerSymbol[ -60, 2 n + 1];

PROG

(PARI) {a(n) = kronecker( -60, 2*n + 1)};

CROSSREFS

Cf. A080891.

Sequence in context: A010059 A143580 A011749 * A104105 A143221 A126999

Adjacent sequences:  A188575 A188576 A188577 * A188579 A188580 A188581

KEYWORD

sign

AUTHOR

Michael Somos, Apr 04 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 23:03 EST 2016. Contains 278900 sequences.