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Search: id:A016103
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| A016103 |
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Expansion of 1/((1-4x)(1-5x)(1-6x)). |
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+0
2
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| 1, 15, 151, 1275, 9751, 70035, 481951, 3216795, 20991751, 134667555, 852639151, 5343198315, 33212784151, 205111785075, 1260114546751, 7708980203835, 46999640806951, 285743822630595, 1733261544204751
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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2*a(n-2) = 6^n-2*5^n+4^n is the number of 3 X n {0,1}-matrices such that: (a) first and second row have a common 1, (b) first and third row have a common 1, (c) second and third row have no a common 1. - Andy Fugard (a.fugard(AT)ed.ac.uk) and Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 26 2008
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LINKS
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Andy Fugard, Counting first-order models (with n individuals) of syllogisms.
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FORMULA
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a(n) = (4^n + 6^n - 2*5^n) /2. - Andy Fugard, Jul 22 2008
If we define f(m,j,x)=sum(binomial(m,k)*stirling2(k,j)*x^(m-k),k=j..m) then a(n-2)=f(n,2,4), (n>=2). [From Milan R. Janjic (agnus(AT)blic.net), Apr 26 2009]
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CROSSREFS
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Cf. A051588.
Sequence in context: A081135 A084902 A021364 this_sequence A041424 A021124 A004322
Adjacent sequences: A016100 A016101 A016102 this_sequence A016104 A016105 A016106
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com)
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