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A055842
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A second order recursive sequence.
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3
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1, 3, 16, 80, 400, 2000, 10000, 50000, 250000, 1250000, 6250000, 31250000, 156250000, 781250000, 3906250000, 19531250000, 97656250000, 488281250000, 2441406250000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| First differences of A005054.
For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5} 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} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan R. Janjic (agnus(AT)blic.net), Apr 19 2007
a(n) is the number of generalized compositions of n when there are 4 *i-1 different types of i, (i=1,2,...). [From Milan R. Janjic (agnus(AT)blic.net), Aug 26 2010]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| a(n)=16*5^(n-2), a(0)=1, a(1)=3.
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EXAMPLE
| a(n)=5a(n-1)+[(-1)^n]*C(2,2-n). G.f.(x)=(1-x)^2/(1-5x).
a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*3^k. - DELEHAM Philippe, Dec 05 2011
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CROSSREFS
| Cf. A000351 and A005054.
Sequence in context: A003769 A005386 A053572 * A037773 A037661 A072615
Adjacent sequences: A055839 A055840 A055841 * A055843 A055844 A055845
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, May 30 2000
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