A118546 A symmetrical triangle of coefficient weights: A117662 :f(n)=n*(n - 1)*(n - 2)*(n + 3)/12; t(n,m)=f(n - m + 1)*f(m + 1).

9, 42, 42, 120, 196, 120, 270, 560, 560, 270, 525, 1260, 1600, 1260, 525, 924, 2450, 3600, 3600, 2450, 924, 1512, 4312, 7000, 8100, 7000, 4312, 1512, 2340, 7056, 12320, 15750, 15750, 12320, 7056, 2340, 3465, 10920, 20160, 27720, 30625, 27720, 20160

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Aug 25 2008

Keywords

• nonn
• tabl

Comments

Row sums with zeros:

{0, 0, 9, 84, 436, 1660, 5170, 13948, 33748}.

Examples

			Initial Zeros removed:
{9},
{42, 42},
{120, 196, 120},
{270, 560, 560, 270},
{525, 1260, 1600, 1260, 525},
{924, 2450, 3600, 3600, 2450, 924},
{1512, 4312, 7000, 8100, 7000, 4312, 1512},
{2340, 7056, 12320, 15750, 15750, 12320, 7056, 2340},
{3465, 10920, 20160, 27720, 30625, 27720, 20160, 10920, 3465}
		

References

• Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, Inc., New York, 1972, page145: Number of algebraic scalars constructed from curvature R(i,j,k,l) and metric ground form g(i,j):A117662.

Crossrefs

Cf. A117662.

Programs

Mathematica

f[n_] = n*(n - 1)*(n - 2)*(n + 3)/12; t[n_, m_] = f[n - m + 1]*f[m + 1]; Table[Table[t[n, m], {m, 2, n - 2}], {n, 2, 12}]; Flatten[%]

Formula

f(n)=n*(n - 1)*(n - 2)*(n + 3)/12; t(n,m)=f(n - m + 1)*f(m + 1).