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A055841
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Number of compositions of n into 3*j-1 kinds of j's for all j>=1.
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6
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1, 2, 9, 36, 144, 576, 2304, 9216, 36864, 147456, 589824, 2359296, 9437184, 37748736, 150994944, 603979776, 2415919104, 9663676416, 38654705664, 154618822656, 618475290624, 2473901162496, 9895604649984, 39582418599936, 158329674399744, 633318697598976, 2533274790395904, 10133099161583616, 40532396646334464, 162129586585337856, 648518346341351424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| First differences of A002001.
For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan R. Janjic (agnus(AT)blic.net), Apr 19 2007
Convolved with [1, 2, 3,...] = powers of 4: [1, 4, 16, 64,...]. [From Gary W. Adamson, Jun 04 2009]
a(n) is the number of generalized compositions of n when there are 3 *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) = 9*4^(n-2), a(0)=1, a(1)=2.
a(0)=1, a(1)=2, a(3)=9, a(n+1)=4*a(n) for n>=3.
G.f.: (1-x)^2/(1-4*x).
G.f.: 1/(1-sum(j>=1, (3*j-1)*x^j )). [Joerg Arndt, Jul 06 2011]
a(n)=4*a(n-1)+(-1)^n*C(2,2-n).
a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*2^k. - DELEHAM Philippe, Dec 05 2011
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CROSSREFS
| Cf. A000302 and A002001.
Essentially the same as A002063.
Sequence in context: A027995 A077836 A003125 * A037521 A037730 A029874
Adjacent sequences: A055838 A055839 A055840 * A055842 A055843 A055844
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, May 30 2000
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EXTENSIONS
| New name, Joerg Arndt, Jul 06 2011.
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