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A081190
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8th binomial transform of (1,0,1,0,1,.....), A059841.
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6
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1, 8, 65, 536, 4481, 37928, 324545, 2803256, 24405761, 213887048, 1884629825, 16679193176, 148135411841, 1319377419368, 11777507763905, 105319346802296, 943126559710721, 8454906106826888, 75861524447454785, 681125306429182616
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OFFSET
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0,2
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COMMENTS
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a(n) is also the number of words of length n over an alphabet of nine letters, of which a chosen one appears an even number of times. See a comment in A007582, also for the crossrefs. for the 1- to 11- letter word cases. For a formulation in terms of maps see a Geoffrey Critzer comment in A081189. - Wolfdieter Lang, Jul 17 2017
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LINKS
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FORMULA
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a(n) = 16*a(n-1) -63*a(n-2), a(0)=1, a(1)=8.
G.f.: (1-8*x)/((1-7*x)*(1-9*x)).
E.g.f. exp(8*x) * cosh(x).
a(n) = 7^n/2 + 9^n/2.
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MATHEMATICA
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CoefficientList[Series[(1 - 8 x) / ((1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{16, -63}, {1, 8}, 20] (* Harvey P. Dale, Apr 04 2017 *)
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PROG
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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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STATUS
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approved
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