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A164356 Expansion of (1 - x^2)^4 / ((1 - x)^4 * (1 - x^4)) in powers of x. 2
1, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 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

M. Somos, Rational Function Multiplicative Coefficients

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

FORMULA

Euler transform of length 4 sequence [4, -4, 0, 1].

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

a(n) = 4 * b(n) unless n=0 and b(n) is multiplicative with b(2) = 3/2, b(2^e) = 1/2 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. a(2*n + 1) = 4. a(4*n) = 2 unless n=0. a(4*n + 2) = 6.

G.f.: -1 + 4 / (1 - x) - 2 / (1 + x^2).

a(n) = 2 * A068073(n) unless n=0. - Michael Somos, Apr 17 2015

EXAMPLE

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

MATHEMATICA

a[ n_] := -Boole[n == 0] + 4 - If[ EvenQ[n], (-1)^(n/2) 2, 0]; (* Michael Somos, Apr 17 2015 *)

a[ n_] := SeriesCoefficient[ -1 + 4/(1 - x) - 2/(1 + x^2), {x, 0, Abs@n}]; (* Michael Somos, Jan 07 2019 *)

PROG

(PARI) {a(n) = -(n==0) + 4 - if( n%2 == 0, (-1)^(n/2) * 2, 0)};

CROSSREFS

Cf. A068073.

Sequence in context: A131890 A062751 A135911 * A181774 A291379 A001138

Adjacent sequences:  A164353 A164354 A164355 * A164357 A164358 A164359

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Aug 13 2009

STATUS

approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)