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A055274
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First differences of 8^n (A001018).
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9
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1, 7, 56, 448, 3584, 28672, 229376, 1835008, 14680064, 117440512, 939524096, 7516192768, 60129542144, 481036337152, 3848290697216, 30786325577728, 246290604621824, 1970324836974592, 15762598695796736, 126100789566373888, 1008806316530991104
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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} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6,7,8} 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 7 types of each natural number. - Milan Janjic, Aug 13 2010
For n>0, a(n) is not the sum of two nonnegative cubes. - Bruno Berselli, Mar 20 2012
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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.
F. Conti, R. Dvornicich, T. Franzoni and S. Mortola, Il Fibonacci N. 0 (included in Il Fibonacci, Unione Matematica Italiana, 2011), 1990, Problem 0.12.4 (see Berselli's comment).
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LINKS
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FORMULA
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G.f.: (1-x)/(1-8*x).
G.f.: 1/( 1 - 7*Sum_{k>=1} x^k ).
a(n) = 7*8^(n-1); a(0)=1.
a(n) = 8*a(n-1) + (-1)^n * C(1, 1-n).
a(n) = 7*Sum_{k=0..n-1} a(k), for n>=1. - Adi Dani, Jun 24 2011
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MAPLE
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MATHEMATICA
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PROG
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(PARI) my(x='x+O('x^66)); Vec((1-x)/(1-8*x)) /* Joerg Arndt, Jun 25 2011 */
(Magma) [1] cat [7*8^(n-1): n in [1..20]]; // G. C. Greubel, Mar 16 2020
(Sage) [1]+[7*8^(n-1) for n in (1..20)] # G. C. Greubel, Mar 16 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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