%I A077415
%S A077415 0,5,16,35,64,105,160,231,320,429,560,715,896,1105,1344,1615,1920,2261,
%T A077415 2640,3059,3520,4025,4576,5175,5824,6525,7280,8091,8960,9889,10880,
%U A077415 11935,13056,14245,15504,16835,18240,19721,21280,22919,24640,26445
%N A077415 Number of independent components of a certain 3-tensor in n-space.
%C A077415 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 
               and t(a,b,c)+t(b,c,a)+t(c,a,b)=0, with a,b,c range 1..n. (3-tensor 
               in n-dimensional space which is symmetric and traceless in one pair 
               of its indices and satisfies the cyclic identity.)
%C A077415 Number of standard tableaux of shape (n-1,2,1) (n>=3). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), May 13 2004
%C A077415 a(n) = A084990(n - 1) - 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 20 2007
%C A077415 Zero followed by partial sums of A028387, starting at n=1. [From Klaus 
               Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 21 2008]
%F A077415 a(n)= n*(n+2)*(n-2)/3 = A077414(n)-binomial(n+2, 3). binomial(n+2, 3)=A000292(n-1).
%F A077415 G.f.: x^3*(5-4*x+x^2)/(1-x)^4.
%p A077415 seq (((n^3)-4*n)/3, n=2..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 20 2007
%p A077415 a:=n->sum(sum(sum(5, j=0..n), k=2..n),m=4..n)/15: seq(a(n), n=3..36); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
%p A077415 seq(sum(n^2-4, k=1..n)/3, n=2..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 28 2008
%t A077415 lst={};s=0;Do[s+=n^2-n-1;AppendTo[lst, s], {n, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Sep 30 2008]
%t A077415 Table[((n-1)*n*(n+1)-(n-1)-n-(n+1))/3,{n,-6,60}] [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Nov 18 2009]
%o A077415 (PARI) {a=0; print1(a,","); for(n=1, 42, print1(a=a+n+(n+1)^2, ","))} 
               [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 21 2008]
%Y A077415 Cf. A028387 (n + (n+1)^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Oct 21 2008]
%Y A077415 Sequence in context: A131425 A096941 A098404 this_sequence A108966 A072333 
               A055232
%Y A077415 Adjacent sequences: A077412 A077413 A077414 this_sequence A077416 A077417 
               A077418
%K A077415 nonn,easy,new
%O A077415 2,2
%A A077415 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 
               2002
%E A077415 More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 20 2007