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A004054
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Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)).
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2
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1, 3, 11, 35, 111, 343, 1051, 3195, 9671, 29183, 87891, 264355, 794431, 2386023, 7163531, 21501515, 64526391, 193622863, 580955971, 1743042675, 5229477551, 15689131703, 47068793211, 141209175835
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
X. Acloque, Polynexus Numbers and other mathematical wonders [broken link]
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FORMULA
| The sequence 0, 0, 1... has a(n)=sum{k=0..floor(n/2), comb(n, 2k)A001045(2k) }. a(n)=3^n/6+(-1)^n/6-0^n/6-2^n/6 - Paul Barry (pbarry(AT)wit.ie), Sep 13 2003
a(n)=3^n-2^n-(-1^(n-1)) a(n)= A001047 -(-1^(n-1)) - Xavier Acloque Oct 17 2003
The signed sequence 0, 1, -3, ... has G.f.: x(1+x)/((1-x)(1+2x)(1+3x) and a(n)=1/6+(-2)^n/3-(-3)^n/2. It is the third inverse binomial transform of A001045(2n-1)-0^n/2. - Paul Barry (pbarry(AT)wit.ie), Apr 21 2004
Convolution of A000244 and A078008. a(n)=sum{k=0..n, A078008(k)3^(n-k)}; a(n)=(3*A00244(n)-A001045(n+2))/2. - Paul Barry (pbarry(AT)wit.ie), Jul 22 2004
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PROG
| (MAGMA) [Ceiling(3^(n+2)/6+(-1)^(n+2)/6-0^n/6-2^(n+2)/6) : n in [0..30]]; // Vincenzo Librandi, Oct 08 2011
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CROSSREFS
| Cf. A001047.
Sequence in context: A026125 A026154 A025181 * A068995 A109196 A032637
Adjacent sequences: A004051 A004052 A004053 * A004055 A004056 A004057
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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