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A016103
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Expansion of 1/((1-4x)(1-5x)(1-6x)).
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
This is the third column of the Sheffer triangle A143496 (4-restricted Stirling2 numbers). See A193685 for general comments. [From Wolfdieter Lang, Oct 08 2011]
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LINKS
| Andy Fugard, Counting first-order models (with n individuals) of syllogisms.
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FORMULA
| 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]
O.g.f.:1/((1-4*x)*(1-5*x)(1-6*x)).
E.g.f.: diff(exp(4*x)*((exp(x)-1)^2)/2!,x$2). See the Sheffer triangle comment above. [From Wolfdieter Lang, Oct 08 2011]
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CROSSREFS
| Cf. A051588, A000302, A005060, A003468.
Sequence in context: A084902 A021364 A206366 * A206361 A041424 A021124
Adjacent sequences: A016100 A016101 A016102 * A016104 A016105 A016106
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com)
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