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A083858
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Expansion of x/(1-3x-6x^2).
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13
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0, 1, 3, 15, 63, 279, 1215, 5319, 23247, 101655, 444447, 1943271, 8496495, 37149111, 162426303, 710173575, 3105078543, 13576277079, 59359302495, 259535569959, 1134762524847, 4961500994295, 21693078131967, 94848240361671
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of A015443. A row of array A083857.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,6).
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FORMULA
| a(n)=3a(n-1)+6a(n-2), a(0)=0, a(1)=1; a(n)=(3sqrt(33)/2+21/2)^(n/2)/sqrt(33)-(21/2-3sqrt(33)/2)^(n/2)(-1)^n/sqrt(33).
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 2}, {1, -4}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2010]
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PROG
| (Other) sage: [lucas_number1(n, 3, -6) for n in xrange(0, 24)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
| Cf. A015523, A015524.
Sequence in context: A103454 A111303 A118339 * A151241 A080948 A098102
Adjacent sequences: A083855 A083856 A083857 * A083859 A083860 A083861
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 06 2003
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