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A055996
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a(n) = 81*10^(n-2), a(0)=1, a(1)=8.
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2
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1, 8, 81, 810, 8100, 81000, 810000, 8100000, 81000000, 810000000, 8100000000, 81000000000, 810000000000, 8100000000000, 81000000000000, 810000000000000, 8100000000000000, 81000000000000000, 810000000000000000
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OFFSET
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0,2
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COMMENTS
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For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8,9,10} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7,8,9,10} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan Janjic, Apr 19 2007
a(n) is the number of generalized compositions of n when there are 9*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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a(n)=10a(n-1)+[(-1)^n]*C(2, 2-n). G.f.(x)=(1-x)^2/(1-10x).
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MATHEMATICA
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Join[{1, 8}, NestList[10#&, 81, 20]] (* Harvey P. Dale, Nov 20 2015 *)
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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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