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A088139
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a(n)=2a(n-1)-6a(n-2), a(0)=0, a(1)=1.
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5
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0, 1, 2, -2, -16, -20, 56, 232, 128, -1136, -3040, 736, 19712, 35008, -48256, -306560, -323584, 1192192, 4325888, 1498624, -22958080, -54907904, 27932672, 385312768, 603029504, -1105817600, -5829812224, -5024718848, 24929435648, 80007184384
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: x/(1-2x+6x^2); e.g.f.: exp(x)sin(sqrt(5)x)/sqrt(5); a(n)=((1+isqrt(5))^n-(1-isqrt(5))^n)/(2isqrt(5)); a(n)=Im{(1+isqrt(5))^n/sqrt(5)}; a(n)=sum{k=0..floor(n/2), C(n, 2k+1)(-5)^k}.
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=2*b-6*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 17 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 2, 6) for n in xrange(0, 30)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
| Cf. A084102, A088136, A088137, A045873.
Sequence in context: A016740 A193145 A133922 * A152556 A113123 A177832
Adjacent sequences: A088136 A088137 A088138 * A088140 A088141 A088142
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 20 2003
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