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A036240
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Number of 3-way interactions when 3 subsets of power set on {1..n} are chosen at random; number of Boolean functions of n variables and rank 3 from Post class F(8,inf).
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6
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0, 0, 12, 200, 2280, 22420, 205212, 1806000, 15522960, 131383340, 1100093412, 9138243400, 75445046040, 619838752260, 5072272077612, 41371548418400, 336519691295520, 2730963319321180, 22119245290765812, 178854325039467000, 1444135501669535400
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OFFSET
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1,3
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REFERENCES
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W. W. Kokko, "Interactions", manuscript, 1983.
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LINKS
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FORMULA
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a(n) = (8^n-7^n-3*4^n+3*3^n+2*2^n-2)/6.
G.f.: 4*x^3*(43*x^2-25*x+3) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(7*x-1)*(8*x-1)). - Colin Barker, Dec 10 2012
a(n) = 25*a(n-1)-241*a(n-2)+1135*a(n-3)-2734*a(n-4)+3160*a(n-5)-1344*a(n-6). - Wesley Ivan Hurt, Oct 23 2014
E.g.f.: exp(x)*(exp(x) - 1)^3*(exp(x) + 1)^2*(exp(2*x) + 2)/6. - Stefano Spezia, Jul 29 2022
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MAPLE
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MATHEMATICA
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CoefficientList[Series[4 x^2 (43 x^2 - 25 x + 3)/((x - 1) (2 x - 1) (3 x - 1) (4 x - 1) (7 x - 1) (8 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 21 2013 *)
LinearRecurrence[{25, -241, 1135, -2734, 3160, -1344}, {0, 0, 12, 200, 2280, 22420}, 30] (* Harvey P. Dale, Dec 29 2013 *)
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PROG
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(PARI) a(n) = (1/3!)*(8^n-7^n-3*4^n+3*3^n+2*2^n-2); \\ Joerg Arndt, Oct 21 2013
(Magma) [(8^n-7^n-3*4^n+3*3^n+2*2^n-2)/6 : n in [1..30]]; // Wesley Ivan Hurt, Oct 23 2014
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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