0,1

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

R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6

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.

G.f.: ( 6 - 4 x + x^2 ) ( 1 - x )^-4.

(1/2) n * (n+2) * (n+3), n>0.

sum (((n+j-1)^2-(n-j+1)^2)/4,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 13 2006

a(n)=sum(k*(n+1), k=2..n, n>=2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2008

seq((n-2)*binomial(n+1, 2), n=3..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 28 2007

a:=n->1/2*sum(sum(sum(1, j=1..n), k=2..n), m=4..n): seq(a(n), n=4..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007

A005564:=(6-4*z+z**2)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]

for n from 2 to 31 do printf(`%d, `, sum(k*(n+1), k=2..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2008

a:=n->add(binomial(n, 2)+add(n, j=2..n), j=2..n-2):seq(a(n)/3, n=4..40); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]

with(combinat):seq(n*numbcomb(n+3, 2), n=1..31); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 17 2009]

f[n_]:=3*n-1; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; If[s2>0, AppendTo[lst, s2]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 27 2009]

First differences of A001701.

Sequence in context: A093913 A006137 A048969 this_sequence A011928 A055455 A050768

Adjacent sequences: A005561 A005562 A005563 this_sequence A005565 A005566 A005567

nonn

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

Added more terms - Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 27 2009