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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). 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 (list; table; graph; refs; listen; history; text; internal format)
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 * A287861 A242356 A165966

Adjacent sequences:  A129364 A129365 A129366 * A129368 A129369 A129370

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

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Last modified July 22 08:27 EDT 2019. Contains 325216 sequences. (Running on oeis4.)