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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
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listen;
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internal format)
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OFFSET
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1,2
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COMMENTS
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First term of n-th row is n*(n+1)/2.
Row sum are A002663 (without initial zeros).
Appears to be the triangle resulting from adding the row number (first row numbered 0) of Pascal's 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 outer two layers, which consist entirely of 0's.
Each value of the sequence T(x,y) is equal to the sum of all values in A014430 that are in the rectangle defined by the tip (0,0) and the position (x,y). - Jon Perry, Sep 11 2013
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LINKS
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FORMULA
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EXAMPLE
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Table begins
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
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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
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KEYWORD
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nonn,tabf,uned
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AUTHOR
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STATUS
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approved
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