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A164115 Expansion of (1 - x^5) / ((1 - x) * (1 - x^4)) in powers of x. 3
1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The sequence A107453 has the same terms but different offset.

Convolution inverse of A164116.

LINKS

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

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

FORMULA

Euler transform of length-5 sequence [ 1, 0, 0, 1, -1].

a(n) is multiplicative with a(2) = 1, a(2^e) = 2 if e>1, a(p^e) = 1 if p>2.

a(n) = (-1)^n * A164117(n).

a(4*n) = 2 unless n=0. a(2*n + 1) = a(4*n + 2) = 1.

a(-n) = a(n). 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) = A138191(n+2), n>0. - R. J. Mathar, Aug 17 2009

Dirichlet g.f. (1+1/4^s)*zeta(s). - R. J. Mathar, Feb 24 2011

a(n) = (i^n + (-i)^n + (-1)^n + 5)/4 for n > 0 where i is the imaginary unit. - Bruno Berselli, Feb 25 2011

EXAMPLE

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+x^2+x^3+x^4)/(1-x^4), {x, 0, 100}], x] (* G. C. Greubel, Sep 22 2018 *)

LinearRecurrence[{0, 0, 0, 1}, {1, 1, 1, 1, 2}, 120] (* or *) PadRight[{1}, 120, {2, 1, 1, 1}] (* Harvey P. Dale, Aug 24 2019 *)

PROG

(PARI) {a(n) = 2 - (n==0) - (n%4>0)}

(PARI) x='x+O('x^99); Vec((1-x^5)/((1-x)*(1-x^4))) \\ Altug Alkan, Sep 23 2018

(MAGMA) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x+x^2+x^3+x^4)/(1-x^4))); // G. C. Greubel, Sep 22 2018

CROSSREFS

Cf. A107453, A138191, A164116, A164117.

Sequence in context: A186006 A236398 A107453 * A164117 A177704 A138191

Adjacent sequences:  A164112 A164113 A164114 * A164116 A164117 A164118

KEYWORD

nonn,mult,easy

AUTHOR

Michael Somos, Aug 10 2009

STATUS

approved

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Last modified September 18 09:59 EDT 2019. Contains 327170 sequences. (Running on oeis4.)