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A164359
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Expansion of (1 - x^2)^3 / ((1 - x)^3 * (1 - x^3)) in powers of x.
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1
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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; internal format)
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OFFSET
| 0,2
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FORMULA
| Euler transform of length 3 sequence [ 3, -3, 1].
Moebius transform is length 3 sequence [ 3, 0, -1].
a(-n) = a(n). 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) ).
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EXAMPLE
| 1 + 3*x + 3*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 2*x^6 + 3*x^7 + 3*x^8 + ...
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PROG
| (PARI) {a(n) = -(n==0) + 2 + kronecker(9, n)}
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CROSSREFS
| Sequence in context: A075017 A060586 A076662 * A178307 A079063 A031352
Adjacent sequences: A164356 A164357 A164358 * A164360 A164361 A164362
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 13 2009
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