%I A005564 M4134
%S A005564 6,20,45,84,140,216,315,440,594,780,1001,1260,1560,1904,2295,2736,3230,
%T A005564 3780,4389,5060,5796,6600,7475,8424,9450,10556,11745,13020,14384,15840,
%U A005564 17391,19040,20790,22644,24605,26676,28860,31160,33579,36120,38786
%N A005564 Number of walks on square lattice.
%D A005564 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005564 R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">J. Integer Seqs., Vol. 3 (2000), #00.1.6</
               a>
%H A005564 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 A005564 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.
%F A005564 G.f.: ( 6 - 4 x + x^2 ) ( 1 - x )^-4.
%F A005564 (1/2) n * (n+2) * (n+3), n>0.
%F A005564 sum (((n+j-1)^2-(n-j+1)^2)/4,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Sep 13 2006
%F A005564 a(n)=sum(k*(n+1), k=2..n, n>=2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 29 2008
%p A005564 seq((n-2)*binomial(n+1,2), n=3..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 28 2007
%p A005564 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
%p A005564 A005564:=(6-4*z+z**2)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]
%p A005564 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
%p A005564 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]
%p A005564 with(combinat):seq(n*numbcomb(n+3,2), n=1..31);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 17 2009]
%t A005564 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]
%Y A005564 First differences of A001701.
%Y A005564 Sequence in context: A093913 A006137 A048969 this_sequence A011928 A055455 
               A050768
%Y A005564 Adjacent sequences: A005561 A005562 A005563 this_sequence A005565 A005566 
               A005567
%K A005564 nonn
%O A005564 0,1
%A A005564 N. J. A. Sloane (njas(AT)research.att.com).
%E A005564 Added more terms - Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 27 
               2009