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A098150
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a(n) = 2(a(n-2) - a(n-1)) + a(n-3) where a(0)=-3, a(1)=11 & a(2)=-30.
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2
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-3, 11, -30, 79, -207, 542, -1419, 3715, -9726, 25463, -66663, 174526, -456915, 1196219, -3131742, 8199007, -21465279, 56196830, -147125211, 385178803, -1008411198, 2640054791, -6911753175, 18095204734, -47373861027, 124026378347
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Sequence relates bisections of Lucas and Fibonacci numbers.
2*A098149(n) + a(n) = 8*(-1)^(n+1)*A001519(n) - (-1)^(n+1)*A005248(n+1).
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = - 3a(n-1) - a(n-2). - Tanya Khovanova (tanyakh(AT)yahoo.com), Feb 02 2007
G.f.: (2x-3)/(1+3x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]
a(n)=-(3/2)*[(-3/2)-(1/2)*sqrt(5)]^n-(13/10)*[(-3/2)-(1/2)*sqrt(5)]^n*sqrt(5)+(13/10)*[(-3/2)+(1/2) *sqrt(5)]^n*sqrt(5)-(3/2)*[(-3/2)+(1/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
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MATHEMATICA
| a[0] = -3; a[1] = 11; a[2] = -30; a[n_] := a[n] = 2(a[n - 2] - a[n - 1]) + a[n - 3]; Table[ a[n], {n, 0, 25}] (from Robert G. Wilson v Sep 04 2004)
RecurrenceTable[{a[0]==-3, a[1]==11, a[2]==-30, a[n]==2(a[n-2]-a[n-1])+ a[n-3]}, a, {n, 30}] (* or *) LinearRecurrence[{-3, -1}, {-3, 11}, 30] (* From Harvey P. Dale, Feb 05 2012 *)
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CROSSREFS
| Cf. A098149, A001519, A005248.
Sequence in context: A009183 A165893 A106397 * A167375 A085376 A196233
Adjacent sequences: A098147 A098148 A098149 * A098151 A098152 A098153
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KEYWORD
| easy,sign,changed
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 29 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 04 2004
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