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A015553
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Expansion of x/(1-6x-11x^2).
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5
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0, 1, 6, 47, 348, 2605, 19458, 145403, 1086456, 8118169, 60660030, 453260039, 3386820564, 25306783813, 189095729082, 1412948996435, 10557746998512, 78888920951857, 589468742694774, 4404590586639071, 32911699689476940
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let the generator matrix for the binary Golay G_24 code be [I|B]. Then a(n)=(A^n)_1,2 for instance. Third binomial transform of (0,1,0,20,0,400,0,8000,....). - Paul Barry (pbarry(AT)wit..ie), Feb 13 2004
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,11).
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FORMULA
| a(n) = 6 a(n-1) + 11 a(n-2).
a(n)=(1/4)*sum(k=0, n, binomial(n, k)*Fibonacci(k)*4^k) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 25 2003
a(n)=sqrt(5)(3+2sqrt(5))^n/20-sqrt(5)(3-2sqrt(5))^n/20 - Paul Barry (pbarry(AT)wit..ie), Feb 13 2004
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 4}, {1, -7}}, 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, 6, -11) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
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CROSSREFS
| Cf. A015551.
Sequence in context: A027012 A160609 A024076 * A071878 A104256 A192887
Adjacent sequences: A015550 A015551 A015552 * A015554 A015555 A015556
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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