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A164359 Expansion of (1 - x^2)^3 / ((1 - x)^3 * (1 - x^3)) in powers of x. 3
1, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

FORMULA

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

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

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

G.f.: -1 + (1/3) * ( 8 / (1 - x) - (2 + x) / (1 + x + x^2) ).

a(n) = A244893(n) if n>1. - Michael Somos, Apr 17 2015

EXAMPLE

G.f. = 1 + 3*x + 3*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 2*x^6 + 3*x^7 + 3*x^8 + 2*x^9 + ...

MATHEMATICA

a[ n_] := -Boole[n == 0] + 2 + KroneckerSymbol[ 9, n]; (* Michael Somos, Apr 17 2015 *)

PROG

(PARI) {a(n) = -(n==0) + 2 + kronecker(9, n)};

CROSSREFS

Cf. A244893.

Sequence in context: A075017 A060586 A076662 * A178307 A079063 A031352

Adjacent sequences:  A164356 A164357 A164358 * A164360 A164361 A164362

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Aug 13 2009

STATUS

approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)