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A022308
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a(n) = a(n-1) + a(n-2) + 1 for n>1, a(0)=0, a(1)=3.
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5
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0, 3, 4, 8, 13, 22, 36, 59, 96, 156, 253, 410, 664, 1075, 1740, 2816, 4557, 7374, 11932, 19307, 31240, 50548, 81789, 132338, 214128, 346467, 560596, 907064, 1467661, 2374726, 3842388, 6217115, 10059504, 16276620, 26336125, 42612746, 68948872, 111561619
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: x*(3-2*x) / (x^3-2*x+1).
a(n) = 2*a(n-1) - a(n-3) for n>=3. - Ron Knott, Aug 25 2006
a(n) = (-10 + (5-7*sqrt(5))*((1-sqrt(5))/2)^n + ((1+sqrt(5))/2)^n*(5+7*sqrt(5))) / 10. - Colin Barker, Feb 20 2017
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MAPLE
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with(combinat): seq(fibonacci(n)+fibonacci(n+5)-1, n=-2..30); # Zerinvary Lajos, Feb 01 2008
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MATHEMATICA
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CoefficientList[Series[x (3 - 2 x)/(x^3 - 2 x + 1), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 26 2018 *)
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PROG
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(PARI) concat(0, Vec(x*(3-2*x)/(x^3-2*x+1) + O(x^50))) \\ Colin Barker, Feb 20 2017
(PARI) a(n) = if(n==0, 0, if(n==1, 3, a(n-1)+a(n-2)+1)) \\ Felix Fröhlich, Mar 26 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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