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A153773
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a(2*n) = 3*a(2*n-1) - 1, a(2*n+1) = 3*a(2*n), with a(1)=1.
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6
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1, 2, 6, 17, 51, 152, 456, 1367, 4101, 12302, 36906, 110717, 332151, 996452, 2989356, 8968067, 26904201, 80712602, 242137806, 726413417, 2179240251, 6537720752, 19613162256, 58839486767, 176518460301, 529555380902, 1588666142706, 4765998428117, 14297995284351
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3).
G.f.: x*(-1 + x + x^2)/((1-x) * (3*x-1) * (1+x)).
a(n) = (5*3^n + 6 - 3*(-1)^n)/24. (End)
E.g.f.: (1/24)*(-3*exp(-x) - 8 + 6*exp(x) + 5*exp(3*x)). - G. C. Greubel, Aug 27 2016
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EXAMPLE
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a(2) = 3*1 - 1 = 2.
a(3) = 3*a(2) = 6.
a(4) = 3*a(3) - 1 = 17.
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MATHEMATICA
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Table[(5*3^n + 6 - 3*(-1)^n)/24 , {n, 1, 25}] (* or *) LinearRecurrence[{3, 1, -3}, {1, 2, 6}, 25] (* G. C. Greubel, Aug 27 2016 *)
RecurrenceTable[{a[1] == 1, a[2] == 2, a[3] == 6, a[n] == 3 a[n-1] + a[n-2] - 3 a[n-3]}, a, {n, 30}] (* Vincenzo Librandi, Aug 28 2016 *)
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PROG
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(Magma) I:=[1, 2, 6]; [n le 3 select I[n] else 3*Self(n-1)+Self(n-2)-3*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Aug 28 2016
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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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