0,5

For n>4, number of simple rank-(n-1) matroids over S_n.

Number of non-interval subsets of {1,2,3,...,n} (cf. A000124). - Jose Luis Arregui (arregui(AT)unizar.es), Jun 27 2006

The partial sums of the second diagonal of A008292 or third column of A123125. [From Tom Copeland (tcjpn(AT)msn.com), Sep 09 2008]

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

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.)

J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. f. Math., 73 (1969), 7-30.

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.

W. M. B. Dukes, On the number of matroids on a finite set

G.f.: x^3/((1-2*x)*(1-x)^3).

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

a(n)=2a(n-1)+C(n, 2) - Paul Barry (pbarry(AT)wit.ie), Aug 23 2004

(1, 5, 16, 42, 99,...) = binomial transform of (1, 4, 7, 8, 8, 8,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 30 2007

E.g.f.:exp(x)[exp(x)-x^2/2-x-1] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Feb 11 2009]

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

A002662:=z**2/(2*z-1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]

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]

Table[Sum[ Binomial[n + 3, k + 3], {k, 0, n}], {n, -3, 30}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]

Table[Sum[Binomial[n, i], {i, 3, n}], {n, 0, 41}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]

a(n)= A055248(n, 3). Partial sums of A000295.

Cf. A000079, A000225, A000295, A002663, A002664, A035038-A035042.

Sequence in context: A014175 A097810 A055796 this_sequence A143962 A066634 A034358

Adjacent sequences: A002659 A002660 A002661 this_sequence A002663 A002664 A002665

easy,nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).