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A055846
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a(n) = 25*6^(n-2), with a(0)=1 and a(1)=4.
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1
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1, 4, 25, 150, 900, 5400, 32400, 194400, 1166400, 6998400, 41990400, 251942400, 1511654400, 9069926400, 54419558400, 326517350400, 1959104102400, 11754624614400, 70527747686400, 423166486118400, 2538998916710400
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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} 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} 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 5*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) = 25*6^(n-2), a(0)=1, a(1)=4. a(n) = 6a(n-1) + ((-1)^n)*binomial(2, 2-n); g.f.(x)=(1-x)^2/(1-6x).
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MATHEMATICA
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LinearRecurrence[{6}, {1, 4, 25}, 30] (* Harvey P. Dale, May 25 2023 *)
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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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EXTENSIONS
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STATUS
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approved
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