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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
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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} 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 Janjic, Apr 19 2007
Convolved with [1, 2, 3, ...] = powers of 4: [1, 4, 16, 64, ...]. - 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,...). - 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) = 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).
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MATHEMATICA
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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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