A129367 A symmetrical triangle of coefficient weights: A002415 :f(n)=n^2*(n^2 - 1)/12; t(n,m)=f(n - m + 1)*f(m + 1).

36, 120, 120, 300, 400, 300, 630, 1000, 1000, 630, 1176, 2100, 2500, 2100, 1176, 2016, 3920, 5250, 5250, 3920, 2016, 3240, 6720, 9800, 11025, 9800, 6720, 3240, 4950, 10800, 16800, 20580, 20580, 16800, 10800, 4950, 7260, 16500, 27000, 35280, 38416

Offset

1,1

Comments

Row sums with zeros:

{0, 0, 36, 240, 1000, 3260, 9052, 22372, 50545}.

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 components from curvature R(i,j,k,l) :A002415.

Links

Table of n, a(n) for n=1..41.

Formula

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

Example

Initial Zeros removed:
{36},
{120, 120},
{300, 400, 300},
{630, 1000, 1000, 630},
{1176, 2100, 2500, 2100, 1176},
{2016, 3920, 5250, 5250, 3920, 2016},
{3240, 6720, 9800, 11025, 9800, 6720, 3240},
{4950, 10800, 16800, 20580, 20580, 16800, 10800, 4950},
{7260, 16500, 27000, 35280, 38416, 35280, 27000, 16500, 7260}

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[%]

Crossrefs

Cf. A117662, A002415.

Sequence in context: A033575 A044287 A044668 * A350500 A287861 A242356

Adjacent sequences: A129364 A129365 A129366 * A129368 A129369 A129370

Keyword

nonn,tabl

Author

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

Status

approved