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A164358 Expansion of (1 - x^2)^2 * (1 - x^3) / ((1 - x)^3 * (1 - x^4)) in powers of x. 2
1, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 3*b(n) unless n=0 where b(n) is multiplicative with b(2) = 4/3, b(2^e) = 2/3 if e>1, b(p^e) = 1 if p>2.

Euler transform of length 4 sequence [3, -2, -1, 1].

Moebius transform is length 4 sequence [3, 1, 0, -2].

a(n) = a(-n) for all n in Z. a(n+4) = a(n) unless n=0 or n=-4. a(4*n) == 2 unless n=0. a(2*n + 1) = 3. a(4*n + 2) = 4.

G.f.: -1 + 3 / (1 - x) - 1 / (1 + x^2).

EXAMPLE

G.f. = 1 + 3*x + 4*x^2 + 3*x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 3*x^7 + 2*x^8 + ...

MATHEMATICA

a[ n_] := - Boole[n == 0] + 3 - If[ EvenQ[n], (-1)^(n/2), 0];

CoefficientList[Series[(1+3*x+4*x^2+3*x^3+x^4)/(1-x^4), {x, 0, 150}], x] (* G. C. Greubel, Sep 26 2018 *)

PROG

(PARI) {a(n) = -(n==0) + 3 - if( n%2 == 0, (-1)^(n/2), 0)};

(PARI) x='x+O('x^150); Vec((1+3*x+4*x^2+3*x^3+x^4)/(1-x^4)) \\ G. C. Greubel, Sep 26 2018

(MAGMA) m:=150; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x+4*x^2+3*x^3+x^4)/(1-x^4))); // G. C. Greubel, Sep 26 2018

CROSSREFS

Sequence in context: A167877 A280136 A258451 * A275638 A281975 A133617

Adjacent sequences:  A164355 A164356 A164357 * A164359 A164360 A164361

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 13 2009

STATUS

approved

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)