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A083337
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a(n) = 2*a(n-1) + 2*a(n-2); a(0)=0, a(1)=3.
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10
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0, 3, 6, 18, 48, 132, 360, 984, 2688, 7344, 20064, 54816, 149760, 409152, 1117824, 3053952, 8343552, 22795008, 62277120, 170144256, 464842752, 1269974016, 3469633536, 9479215104, 25897697280, 70753824768, 193303044096, 528113737728, 1442833563648, 3941894602752, 10769456332800
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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.: 3x/(1 - 2x - 2x^2).
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MATHEMATICA
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CoefficientList[Series[3x/(1-2x-2x^2), {x, 0, 25}], x]
s = Sqrt[3]; a[n_] := Simplify[s*((1 + s)^n - (1 - s)^n)/2]; Array[a, 30, 0] (* or *)
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PROG
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(Haskell)
a083337 n = a083337_list !! n
a083337_list =
0 : 3 : map (* 2) (zipWith (+) a083337_list (tail a083337_list))
(PARI) apply( a(n)=([1, 1; 3, 1]^n)[2, 1], [0..30]) \\ or: ([2, 2; 1, 0]^n)[2, 1]*3. - M. F. Hasler, Aug 06 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Apr 29 2003
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EXTENSIONS
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Edited and definition completed by M. F. Hasler, Aug 06 2018
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STATUS
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approved
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