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A051375
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Number of Boolean functions of n variables and rank 3 from Post class F(5,inf).
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1
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0, 0, 9, 66, 345, 1590, 6909, 29106, 120465, 493230, 2005509, 8116746, 32744985, 131801670, 529647309, 2125861986, 8525167905, 34165634910, 136857036309, 548010848826, 2193789933225, 8780396200950, 35137287916509
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OFFSET
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1,3
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REFERENCES
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V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
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LINKS
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FORMULA
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a(n) = (4^n - 3^n - 3*2^n + 5)/2.
a(n) = Sum_{j=1..n} (-1)^(j+1)*C(n, j)*C(2^(n-j)-1, k-1) (with k=3).
Also: 1/(k-1)!*Sum(s(k, j)*(2^((j-1)*n)-(2^(j-1)-1)^n), j=1..k), where s(k, j) are Stirling numbers of the first kind (with k=3).
a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).
G.f.: 3*x^3*(3-8*x)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)). (End)
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MATHEMATICA
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Table[(4^n - 3^n - 3*2^n + 5)/2, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
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PROG
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(PARI) for(n=0, 50, print1((4^n - 3^n - 3*2^n + 5)/2, ", ")) \\ G. C. Greubel, Oct 08 2017
(Magma) [(4^n - 3^n - 3*2^n + 5)/2: n in [0..50]]; // G. C. Greubel, Oct 08 2017
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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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