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URL: https://oeis.org/A036240

⇱ A036240 - OEIS

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A036240
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).
6
0, 0, 12, 200, 2280, 22420, 205212, 1806000, 15522960, 131383340, 1100093412, 9138243400, 75445046040, 619838752260, 5072272077612, 41371548418400, 336519691295520, 2730963319321180, 22119245290765812, 178854325039467000, 1444135501669535400
OFFSET
1,3
REFERENCES
W. W. Kokko, "Interactions", manuscript, 1983.
LINKS
V. Jovovic and 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).
Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).
Index entries for linear recurrences with constant coefficients, signature (25,-241,1135,-2734,3160,-1344).
FORMULA
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
MAPLE
A036240:=n->(8^n-7^n-3*4^n+3*3^n+2*2^n-2)/6: seq(A036240(n), n=1..30); # Wesley Ivan Hurt, Oct 23 2014
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A036239.
Sequence in context: A159359 A382040 A119864 * A346509 A355127 A292056
KEYWORD
nonn,easy,nice
STATUS
approved