0,2

Let m(i,1)=i; m(1,j)=j; m(i,j)=m(i-1,j)-m(i-1,j-1); then a(n)=m(n+3,3) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 08 2002

a(n) = number of (n+6)-bit binary sequences with exactly 6 1's none of which is isolated. - David Callan (callan(AT)stat.wisc.edu), Jul 15 2004

If a 2-set Y and 2-set Z, having one element in common, are subsets of an n-set X then a(n-4) is the number of 4-subests of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Oct 03 2007

A008778=Sum of first n Triangular numbers plus previous Triangular number. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 13 2009]

G. E. Andrews, The Theory of Partitions, Add.-Wes. '76, p. 190.

Milan Janjic, Two Enumerative Functions

P. Chinn and S. Heubach, Integer Sequences Related to Compositions without 2's, J. Integer Seqs., Vol. 6, 2003.

a(n) = dot_product(n, n-1, ...2, 1)*(2, 3, ..., n, 1) for n = 2, 3, 4, ... [ i.e. a(2) = (2, 1)*(2, 1), a(3) = (3, 2, 1)*(2, 3, 1). ] (Clark Kimberling)

a(n) = (n+1)*(n^2+8n+6)/6 = a(n-1)+A034856(n+1) = A000297(n-1)+1 = A000217(n)+A000292(n+1) = A000290(n-1)+A000292(n). - Henry Bottomley (se16(AT)btinternet.com), Oct 25 2001

a(n) = Sum{0<=k, l<=n; k+l|n} k*l. - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 06 2005

1+4*k+4*binomial(k, 2)+binomial(k, 3);

with (combinat):a[0]:=0:for n from 1 to 50 do a[n]:=2*a[n-1]-a[n-2]+1 od: seq(a[n]+binomial(n+3, n), n=0..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008

Clear[lst, n, a, f]; f[n_]:=n*(n+1)/2; a=0; lst={}; Do[a+=f[n]; AppendTo[lst, a+f[n-1]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 13 2009]

Cf. A022811-A022817, A024207-A024210.

Column 1 of triangle A094415.

Cf. A002411, A008779.

Adjacent sequences: A008775 A008776 A008777 this_sequence A008779 A008780 A008781

Sequence in context: A018394 A147451 A139595 this_sequence A014813 A160420 A147411

nonn,new

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