1,4

Row sums are: {0, 2, 8, 20, 40, 70, 112, 168, 240, 330, 440, ...}.

The sequence based on a dual overlap of A003991 or the weights of Cartan A_n

Dynkin diagrams ( Cahn above) :

t(n,m)=(n-m)*(m+1)->(n - m)*(m + 1) + (n - (m - 1))*m.

I call these neo-combinations because they are very like the symmetrical commutative/ Abelian group based combinations,

but produced by a Cartan Lie type algebra.

t(n,m)=Floor[T(n,m)/n]:

t[n_, m_] = If[n == m == 0, 0, Floor[(n + 2* m *(-m + n))/n]]

is very like the binomial in form.

R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.

T(n,m)=n+2*m*(n-m).

{0},

{1, 1},

{2, 4, 2},

{3, 7, 7, 3},

{4, 10, 12, 10, 4},

{5, 13, 17, 17, 13, 5},

{6, 16, 22, 24, 22, 16, 6},

{7, 19, 27, 31, 31, 27, 19, 7},

{8, 22, 32, 38, 40, 38, 32, 22, 8},

{9, 25, 37, 45, 49, 49, 45, 37, 25, 9},

{10, 28, 42, 52, 58, 60, 58, 52, 42, 28, 10}

Clear[T, n, m, a]; T[n_, m_] = n + 2* m *(-m + n); a = Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]

Cf. A003991.

Sequence in context: A134447 A093056 A151849 this_sequence A134400 A016095 A165464

Adjacent sequences: A141384 A141385 A141386 this_sequence A141388 A141389 A141390

nonn,uned,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 03 2008