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A124326
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Triangular sequence of Pascal triangle minus A077023 with the zeros removed.
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0
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1, 3, 3, 6, 10, 6, 10, 22, 22, 10, 15, 40, 53, 40, 15, 21, 65, 105, 105, 65, 21, 28, 98, 185, 226, 185, 98, 28, 36, 140, 301, 431, 431, 301, 140, 36, 45, 192, 462, 756, 887, 756, 462, 192, 45, 55, 255, 678, 1246, 1673, 1673, 1246, 678, 255, 55, 66, 330, 960, 1956, 2954
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| First term is n*(n-1)/2 type numbers. Row sum is:A002663 ( without zeros) 1, 6, 22, 64, 163, 382, 848, 1816, 3797, 7814, 15914
Appears to be the triangle resulting from adding the row number (first row numbered 0) of Pascals triangle (A007318) to each entry in that row, subtracting the corresponding entries in the triangle formed by taking the finite diagonals in the multiplication table in order of increasing length (A003991), and removing the the outer two layers which consisit entirely of 0s.
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FORMULA
| t(n,m)=When not zero,A007313-A077023[n,m]
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EXAMPLE
| {1},
{3, 3},
{6, 10, 6},
{10, 22, 22, 10},
{15, 40, 53, 40, 15},
{21, 65, 105, 105, 65, 21},
{28, 98, 185, 226, 185, 98, 28},
{36, 140, 301, 431, 431, 301, 140, 36},
{45, 192, 462, 756, 887, 756, 462, 192, 45}
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MATHEMATICA
| a = Table[Flatten[Table[If[Binomial[m, n] - (1 +n (m - n)) == 0, {}, Binomial[m, n] - (1 + n (m - n))], {n, 0, m}]], {m, 0, 14}]
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CROSSREFS
| Cf. A077028, A007313, A002663.
Sequence in context: A167786 A167787 A185957 * A202970 A205004 A031504
Adjacent sequences: A124323 A124324 A124325 * A124327 A124328 A124329
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KEYWORD
| nonn,uned,tabf
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 26 2007
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