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A124326 T(n,m) = A007318(n,m) - A077028(n,m). 1
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; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
FORMULA
T(n,m) = A007318(n,m) - A077028(n,m) (skipping zeros).
EXAMPLE
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;
..
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}]
CROSSREFS
Sequence in context: A167786 A167787 A185957 * A202970 A205004 A236345
KEYWORD
nonn,tabf,uned
AUTHOR
Roger L. Bagula, Jun 26 2007
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)