%I A077414
%S A077414 0,4,15,36,70,120,189,280,396,540,715,924,1170,1456,1785,2160,2584,3060,
%T A077414 3591,4180,4830,5544,6325,7176,8100,9100,10179,11340,12586,13920,15345,
%U A077414 16864,18480,20196,22015,23940,25974,28120,30381,32760,35260
%N A077414 a(n)=n*(n-1)*(n+2)/2.
%C A077414 Number of independent components of a certain 3-tensor in n-space.
%C A077414 a(n) is the number of independent components of a 3-tensor t(a,b,c) which 
               satisfies t(a,b,c)=t(b,a,c) and sum(t(a,a,c),a=1..n)=0 for all c, 
               with a,b,c range 1..n. (3-tensor in n-dimensional space which is 
               symmetric and traceless in one pair of its indices.)
%F A077414 a(n) = n*(binomial(n+1, 2)-1).
%F A077414 G.f.: (x^2)*(4-x)/(1-x)^4.
%F A077414 sum (n*j,j=2..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 
               12 2006
%F A077414 a(n)=sum(sum(j, j=2..n),k=1..n), n>=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 11 2007
%p A077414 a:=n->sum(sum(j, j=2..n),k=1..n): seq(a(n), n=1..41); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 11 2007
%p A077414 a:=n->sum(sum(binomial(n+1,n)-binomial(j+1,j), j=2..n),k=0..n): seq(a(n), 
               n=2..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 
               2007
%p A077414 with(finance):seq(add(cashflows([n*k,n,k], 0 ),k=0..n),n=0..41); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
%p A077414 a:=n->(sum((numbcomp(n,3)), j=0..n)):seq(a(n), n=2..37); [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
%t A077414 f[n_]:=n*(n-1)*(n+2)/2; s=0;lst={};Do[AppendTo[lst,f[n]],{n,0,5!}];lst 
               [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009]
%Y A077414 Sequence in context: A124150 A054556 A113693 this_sequence A015653 A106199 
               A113289
%Y A077414 Adjacent sequences: A077411 A077412 A077413 this_sequence A077415 A077416 
               A077417
%K A077414 nonn,easy
%O A077414 1,2
%A A077414 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 
               2002
%E A077414 More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 30 
               2006