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A055275
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First differences of 9^n (A001019).
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7
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1, 8, 72, 648, 5832, 52488, 472392, 4251528, 38263752, 344373768, 3099363912, 27894275208, 251048476872, 2259436291848, 20334926626632, 183014339639688, 1647129056757192, 14824161510814728, 133417453597332552, 1200757082375992968, 10806813741383936712
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OFFSET
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0,2
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COMMENTS
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For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5,6,7,8,9} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6,7,8,9} we have f(x)<>y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007
a(n) is the number of compositions of n when there are 8 types of each natural number. [From Milan Janjic, Aug 13 2010]
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
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LINKS
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Table of n, a(n) for n=0..20.
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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EXAMPLE
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G.f.: (1-x)/(1-9x). a(n)=8*9^(n-1); a(0)=1. a(n)=9a(n-1)+[(-1)^n]*C(1,1-n).
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MATHEMATICA
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q = 9; Join[{a = 1}, Table[If[n == 0, a = q*a - 1, a = q*a], {n, 0, 25}]] (* From Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
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CROSSREFS
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Cf. A001019.
Sequence in context: A062541 A057091 A156566 * A155198 A147840 A115970
Adjacent sequences: A055272 A055273 A055274 * A055276 A055277 A055278
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, May 28 2000
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EXTENSIONS
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More terms from James A. Sellers, May 29 2000
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STATUS
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approved
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