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A083694
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a(n)=2a(n-1)+5a(n-2).
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1
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0, 2, 4, 18, 56, 202, 684, 2378, 8176, 28242, 97364, 335938, 1158696, 3997082, 13787644, 47560698, 164059616, 565922722, 1952143524, 6733900658, 23228518936, 80126541162, 276395677004, 953424059818, 3288826504656
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A002533(n)/a(n) converges to sqrt(3/2), n>0. a(n)=2*A002533(n-1)+a(n-1).
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FORMULA
| G.f.: 2x/(1-2x-5x^2). a(n)=(1/sqrt(6))[(1+sqrt(6))^n-(1-sqrt(6))^n].
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MATHEMATICA
| CoefficientList[Series[2x/(1-2x-5x^2), {x, 0, 25}], x]
LinearRecurrence[{2, 5}, {0, 2}, 40] (* or *) With[{c=Sqrt[6]}, Simplify/@ Table[((1-c)^n+c (1-c)^n-(1+c)^n+c (1+c)^n)/(5c), {n, 30}]](* From Harvey P. Dale, Nov 03 2011 *)
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CROSSREFS
| Sequence in context: A045664 A106520 A093045 * A179040 A009679 A007727
Adjacent sequences: A083691 A083692 A083693 * A083695 A083696 A083697
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), May 03 2003
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