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A173997 - OEIS
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A173997
Irregular triangle by columns derived from (1, 2, 3, ...) * (1, 2, 3, ...).
4
1, 2, 3, 2, 4, 4, 5, 6, 3, 6, 8, 6, 7, 10, 9, 4, 8, 12, 12, 8, 9, 14, 15, 12, 5, 10, 16, 18, 16, 10, 11, 18, 21, 20, 15, 6, 12, 20, 24, 24, 20, 12, 13, 22, 27, 28, 25, 18, 7, 14, 24, 30, 32, 30, 24, 14, 15, 26, 33, 36, 35, 30, 21, 8, 16, 28, 36, 40, 40, 36, 28, 16
OFFSET
1,2
COMMENTS
Given a (1, 2, 3, ...) * (1, 2, 3, ...) multiplication table; leftmost column of the triangle = (1, 2, 3, ...). Then shift down each successive column of the array twice to get this irregular triangle.
FORMULA
T(n, k) = k*(2 - 2*k + n), with 1 <= k <= floor((n + 1)/2). - Stefano Spezia, Apr 19 2022
EXAMPLE
Given:
1, 2, 3, 4, 5, ...
2, 4, 6, 8, 10, ...
3, 6, 9, 12, 15, ...
4, 8, 12, 16, 20, ...
...
After the shift twice operation, we obtain:
1;
2;
3, 2;
4, 4;
5, 6, 3;
6, 8, 6;
7, 10, 9, 4;
8, 12, 12, 8;
9, 14, 15, 12, 5;
10, 16, 18, 16, 10;
11, 18, 21, 20, 15, 6;
12, 20, 24, 24, 20, 12;
...
MATHEMATICA
Flatten[Table[k(2-2k+n), {n, 16}, {k, Floor[(n+1)/2]}]] (* Stefano Spezia, Apr 19 2022 *)
CROSSREFS
Cf. A003991, A006918 (row sums).
Sequence in context: A179806 A364346 A182762 * A029143 A363263 A153846
KEYWORD
nonn,easy,tabf
AUTHOR
Gary W. Adamson, Mar 05 2010
STATUS
approved