%I A002662 M3866 N1585
%S A002662 0,0,0,1,5,16,42,99,219,466,968,1981,4017,8100,16278,32647,65399,130918,
%T A002662 261972,524097,1048365,2096920,4194050,8388331,16776915,33554106,67108512,
%U A002662 134217349,268435049,536870476,1073741358,2147483151,4294966767,8589934030
%N A002662 2^n - 1 - n(n+1)/2.
%C A002662 For n>4, number of simple rank-(n-1) matroids over S_n.
%C A002662 Number of non-interval subsets of {1,2,3,...,n} (cf. A000124). - Jose 
               Luis Arregui (arregui(AT)unizar.es), Jun 27 2006
%C A002662 The partial sums of the second diagonal of A008292 or third column of 
               A123125. [From Tom Copeland (tcjpn(AT)msn.com), Sep 09 2008]
%C A002662 a(n) is the number of binary sequences of length n having at least three 
               0's. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Feb 
               11 2009]
%D A002662 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002662 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002662 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.
%D A002662 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VI: Voronoi 
               Reduction of Three-Dimensional Lattices, Proc. Royal Soc. London, 
               Series A, 436 (1992), 55-68. (See Table 1.)
%D A002662 J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. 
               f. Math., 73 (1969), 7-30.
%H A002662 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A002662 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A002662 W. M. B. Dukes, <a href="http://arXiv.org/abs/math.CO/0411557">On the 
               number of matroids on a finite set</a>
%F A002662 G.f.: x^3/((1-2*x)*(1-x)^3).
%F A002662 a(n)=sum{k=0..n, C(n, k+3)} = sum{k=3..n, C(n, k)}. - Paul Barry (pbarry(AT)wit.ie), 
               Jul 30 2004
%F A002662 a(n)=2a(n-1)+C(n, 2) - Paul Barry (pbarry(AT)wit.ie), Aug 23 2004
%F A002662 (1, 5, 16, 42, 99,...) = binomial transform of (1, 4, 7, 8, 8, 8,...). 
               - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 30 2007
%F A002662 E.g.f.:exp(x)[exp(x)-x^2/2-x-1] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Feb 11 2009]
%p A002662 a:=n->sum(binomial(n,2*j),j=2..n): seq(a(n), n=1..34); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 13 2007
%p A002662 A002662:=z**2/(2*z-1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 
               dissertation.]
%t A002662 a=1;lst={};s1=s2=s3=0;Do[s1+=a;s2+=s1;s3+=s2;AppendTo[lst,s3];a=a*2,{n,
               6!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 10 
               2009]
%t A002662 Table[Sum[ Binomial[n + 3, k + 3], {k, 0, n}], {n, -3, 30}] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
%t A002662 Table[Sum[Binomial[n, i], {i, 3, n}], {n, 0, 41}] [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jul 10 2009]
%Y A002662 a(n)= A055248(n, 3). Partial sums of A000295.
%Y A002662 Cf. A000079, A000225, A000295, A002663, A002664, A035038-A035042.
%Y A002662 Sequence in context: A014175 A097810 A055796 this_sequence A143962 A066634 
               A034358
%Y A002662 Adjacent sequences: A002659 A002660 A002661 this_sequence A002663 A002664 
               A002665
%K A002662 easy,nonn,nice
%O A002662 0,5
%A A002662 N. J. A. Sloane (njas(AT)research.att.com).