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A099012
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3^(n-1)*Fibonacci(n).
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15
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0, 1, 3, 18, 81, 405, 1944, 9477, 45927, 223074, 1082565, 5255361, 25509168, 123825753, 601059771, 2917611090, 14162371209, 68745613437, 333698181192, 1619805064509, 7862698824255, 38166342053346, 185263315578333
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform is A057088 (with leading 0). Partial sums are A099013. Binomial transform of A015447 (with leading 0).
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FORMULA
| G.f.: x/(1-3x-9x^2); a(n)=3a(n-1)+9a(n-2); a(n)=sqrt(5)(3/2+3sqrt(5)/2)^n/15-sqrt(5)(3/2-3sqrt(5)/2)^n/15.
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 5}, {1, -4}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
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PROG
| (Sage) [lucas_number1(n, 3, -9) for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
(MAGMA) [3^(n-1)*Fibonacci(n): n in [0..60]]; // Vincenzo Librandi, Apr 23 2011
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CROSSREFS
| Cf. A000045.
Sequence in context: A036290 A078904 * A122069 A103897 A119424 A037295
Adjacent sequences: A099009 A099010 A099011 * A099013 A099014 A099015
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 22 2004
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