2,2

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.)

Number of standard tableaux of shape (n-1,2,1) (n>=3). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2004

a(n) = A084990(n - 1) - 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007

Zero followed by partial sums of A028387, starting at n=1. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 21 2008]

a(n)= n*(n+2)*(n-2)/3 = A077414(n)-binomial(n+2, 3). binomial(n+2, 3)=A000292(n-1).

G.f.: x^3*(5-4*x+x^2)/(1-x)^4.

seq (((n^3)-4*n)/3, n=2..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 20 2007

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

seq(sum(n^2-4, k=1..n)/3, n=2..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 28 2008

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]

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]

(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]

Cf. A028387 (n + (n+1)^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 21 2008]

Sequence in context: A131425 A096941 A098404 this_sequence A108966 A072333 A055232

Adjacent sequences: A077412 A077413 A077414 this_sequence A077416 A077417 A077418

nonn,easy,new

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002

More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007