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A081203
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9th binomial transform of (0,1,0,1,0,1,.....), A000035.
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6
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0, 1, 18, 244, 2952, 33616, 368928, 3951424, 41611392, 432891136, 4463129088, 45705032704, 465640261632, 4725122093056, 47800976744448, 482407813955584, 4859262511644672, 48874100093157376, 490992800745259008
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OFFSET
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0,3
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COMMENTS
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For a combinatorial interpretation of a(n) with special 10-letter words of length n see the comment in A081200 on the 7-letter analog.
The binomial transform of {a(n)}_{n >= 0} is {0, A016190}, the 11-letter analog.
(End)
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LINKS
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FORMULA
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a(n) = 18*a(n-1)-80*a(n-2), a(0)=0, a(1)=1.
G.f.: x/((1-8*x)*(1-10*x)).
a(n) = 10^n/2 - 8^n/2.
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MATHEMATICA
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CoefficientList[Series[x / ((1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{18, -80}, {0, 1}, 20] (* Harvey P. Dale, Aug 05 2018 *)
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PROG
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CROSSREFS
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Apart from the first term, identical to A016186.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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