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A093356
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Number of occurrences of pattern 1-2 after n iterations of morphism A007413.
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1
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3, 8, 28, 104, 400, 1568, 6208, 24704, 98560, 393728, 1573888, 6293504, 25169920, 100671488, 402669568, 1610645504, 6442516480, 25769934848, 103079477248, 412317384704, 1649268490240, 6597071863808, 26388283260928
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = (3*4^(n-1) + 2^n)/2, a(1) = 3.
G.f.: (6 - 20*x + 8*x^2)/((1-2*x)*(1-4*x)).
a(n) = 6*a(n-1) - 8*a(n-2); a(1)=3, a(2)=8, a(3)=28. -Harvey P. Dale, Oct 02 2011
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MATHEMATICA
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Join[{3}, Table[(3*4^(n-1)+2^n)/2, {n, 2, 30}]] (* or *) Join[{3}, LinearRecurrence[ {6, -8}, {8, 28}, 30]] (* Harvey P. Dale, Oct 02 2011 *)
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PROG
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(PARI) a(n)=(3*4^(n-1)+2^n)/2
(Magma) [Ceiling((3*(4^(n-1)) + 2^n)/2): n in [1..30]]; // Vincenzo Librandi, Oct 03 2011
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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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