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A022314
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a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0, a(1) = 9.
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1
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0, 9, 10, 20, 31, 52, 84, 137, 222, 360, 583, 944, 1528, 2473, 4002, 6476, 10479, 16956, 27436, 44393, 71830, 116224, 188055, 304280, 492336, 796617, 1288954, 2085572, 3374527, 5460100, 8834628, 14294729, 23129358, 37424088, 60553447, 97977536, 158530984
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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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a(n) = -1 + (1/2)*((1 + sqrt(5))/2)^n + (19/10)sqrt(5)*((1 + sqrt(5))/2)^n - (19/10)*sqrt(5)*((1 - sqrt(5))/2)^n + (1/2)*((1 - sqrt(5))/2)^n, obtained using PURRS. - Alexander R. Povolotsky, Apr 22 2008
G.f.: -x*(-9+8*x) / ( (x-1)*(x^2+x-1) ).
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EXAMPLE
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G.f. = 9*x + 10*x^2 + 20*x^3 + 31*x^4 + 52*x^5 + 84*x^6 + 137*x^7 + 222*x^8 + ...
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MATHEMATICA
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a[ n_] := 9 Fibonacci[n] + Fibonacci[n + 1] - 1; (* Michael Somos, Nov 21 2016 *)
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PROG
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(PARI) concat(0, Vec(-x*(-9+8*x) / ( (x-1)*(x^2+x-1) ) + O(x^30))) \\ Michel Marcus, Nov 20 2016
{a(n) = 9*fibonacci(n) + fibonacci(n+1) - 1}; /* Michael Somos, Nov 21 2016 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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