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A051180
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Number of 3-element intersecting families of an n-element set.
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19
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0, 0, 0, 13, 222, 2585, 25830, 238833, 2111382, 18142585, 152937510, 1271964353, 10476007542, 85662034185, 696700867590, 5643519669073, 45575393343702, 367206720319385, 2953481502692070, 23723872215168993, 190372457332919862
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = (1/3!)*(8^n - 3*6^n + 3*5^n - 4*4^n + 3*3^n + 2*2^n - 2).
G.f. x^3*(744*x^3 - 606*x^2 + 155*x - 13)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Jul 29 2012
a(0)=0, a(1)=0, a(2)=0, a(3)=13, a(4)=222, a(5)=2585, a(6)=25830, a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7). - Harvey P. Dale, Jul 07 2013
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MAPLE
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seq(1/3!*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2), n=0..40);
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MATHEMATICA
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Table[1/3!(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2), {n, 0, 30}] (* or *) LinearRecurrence[{29, -343, 2135, -7504, 14756, -14832, 5760}, {0, 0, 0, 13, 222, 2585, 25830}, 30] (* Harvey P. Dale, Jul 07 2013 *)
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PROG
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(PARI) for(n=0, 25, print1((1/3!)*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2), ", ")) \\ G. C. Greubel, Oct 06 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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