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A055275
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First differences of 9^n (A001019).
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12
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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, 97261323672455430408, 875351913052098873672
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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. - 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, pp. 194-196.
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LINKS
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FORMULA
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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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MAPLE
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MATHEMATICA
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PROG
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(Magma) [1] cat [8*9^(n-1): n in [1..25]]; // G. C. Greubel, Mar 16 2020
(Sage) [1]+[8*9^(n-1) for n in (1..25)] # G. C. Greubel, Mar 16 2020
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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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