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A165407
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Expansion of 1/(1-x-x^3*c(x^3)), c(x) the g.f. of A000108.
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2
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1, 1, 1, 2, 3, 4, 7, 11, 16, 27, 43, 65, 108, 173, 267, 440, 707, 1105, 1812, 2917, 4597, 7514, 12111, 19196, 31307, 50503, 80380, 130883, 211263, 337284, 548547, 885831, 1417582, 2303413, 3720995, 5965622, 9686617, 15652239, 25130844, 40783083
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Hankel transform is A010892(n+1). Row sums of A165408.
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FORMULA
| G.f.: 2/(1-2x+sqrt(1-4x^3))=1/(1-x-x^3/(1-x^3/(1-x^3/(1-x^3/(1-.... (continued fraction);
a(n)=sum{k=0..n, if(n<=3k, C((n+k)/2,k)*((3k-n)/2+1)(1+(-1)^(n-k))/(2(k+1))};
a(n)=sum{k=0..n+1, F(n-k+1)*(0^k-A000108((k-2)/3)*(1+2*cos(2*pi*(k-2)/3))/3)}.
Conjecture: (n+1)*a(n) -(n+1)*a(n-1) -(n+1)*a(n-2) +2*(7-2*n)*a(n-3) +2*(2*n-7)*a(n-4) +2*(2*n-7)*a(n-5)=0. - R. J. Mathar, Nov 15 2011
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CROSSREFS
| Sequence in context: A113435 A025048 A017987 * A039897 A050193 A173173
Adjacent sequences: A165404 A165405 A165406 * A165408 A165409 A165410
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 17 2009
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