A188578 Expansion of (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15) in powers of x.

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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Michael Somos, Rational Function Multiplicative Coefficients

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1,-1,0,1,-1).

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)};
(Magma) m:=80; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x^3)*(1-x^5)*(1-x^6)/(1-x^15))); // G. C. Greubel, Aug 13 2018

Crossrefs

Cf. A080891.

Sequence in context: A143580 A011749 A277450 * A322217 A104105 A295889

Adjacent sequences: A188575 A188576 A188577 * A188579 A188580 A188581

Keyword

sign,easy

Author

Michael Somos, Apr 04 2011

Status

approved