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A056120
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a(n) = (3^3)*4^(n-3) with a(0)=1, a(1)=1 and a(2)=7.
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2
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1, 1, 7, 27, 108, 432, 1728, 6912, 27648, 110592, 442368, 1769472, 7077888, 28311552, 113246208, 452984832, 1811939328, 7247757312, 28991029248, 115964116992, 463856467968, 1855425871872
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OFFSET
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0,3
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COMMENTS
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For n>=3, 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, x_3 in {1,2,...,n} and fixed y_1, y_2, y_3 in {1,2,3,4} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan Janjic, May 13 2007
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LINKS
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FORMULA
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a(n) = 4*a(n-1) + (-1)^n*binomial(3, 3-n).
G.f.: (1-x)^3/(1-4*x).
E.g.f.: (37 - 44*x + 8*x^2 + 27*exp(4*x))/64. - G. C. Greubel, Jan 18 2020
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MAPLE
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MATHEMATICA
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Table[If[n<2, 1, If[n==2, 7, 27*4^(n-3)]], {n, 0, 25}] (* G. C. Greubel, Jan 18 2020 *)
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PROG
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(PARI) vector(26, n, if(n<2, 1, if(n==2, 7, 27*4^(n-3))) ) \\ G. C. Greubel, Jan 18 2020
(Magma) [1, 1, 7] cat [27*4^(n-3): n in [3..25]]; // G. C. Greubel, Jan 18 2020
(Sage) [1, 1, 7]+[27*4^(n-3) for n in (3..25)] # G. C. Greubel, Jan 18 2020
(GAP) Concatenation([1, 1, 7], List([3..25], n-> 27*4^(n-3) )); # G. C. Greubel, Jan 18 2020
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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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