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A003469
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Number of minimal covers of an n-set.
(Formerly M4153)
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1
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1, 6, 22, 65, 171, 420, 988, 2259, 5065, 11198, 24498, 53157, 114583, 245640, 524152, 1113959, 2359125, 4980546, 10485550, 22019865, 46137091, 96468716, 201326292, 419430075, 872414881, 1811938950, 3758095978, 7784627789, 16106126895, 33285996048
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Hearne and Wagner, Minimal covers of finite sets, Discr. Math. 5 (1973), 247-251.
Math. Mag. vol. 68, n4, p 274 Oct '95.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| G.f.: (1 - x - x^2 ) / ((1 - x )^3*(1 - 2*x)^2).
a(n) = (n+1)*2^n-(n+1)*(n+2)/2 - Paul Barry, Jan 27 2003
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MAPLE
| a:=n->sum(n*binomial(n, k)/2, k=2..n): seq(a(n), n=2..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2007
A003469:=(-1+z+z**2)/(2*z-1)**2/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[(n+1)2^n-(n+1)(n+2)/2, {n, 200}] (* From Vladimir Joseph Stephan Orlovsky, Jun 30 2011 *)
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PROG
| (PARI) a(n) = (n+1)*2^n-(n+1)*(n+2)/2;
(MAGMA) [2^n*(n+1)-(n^2+3*n+2)/2: n in [1..30]]; // Vincenzo Librandi, Aug 19 2011
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CROSSREFS
| Partial sums of A053221.
Cf. A053218.
Sequence in context: A001925 A002663 A099855 * A189418 A027992 A171495
Adjacent sequences: A003466 A003467 A003468 * A003470 A003471 A003472
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Offset changed from 2 to 1 by Vincenzo Librandi, Aug 19 2011
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