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A294317
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Triangle read by rows: T(n, k) = 2*n-k, k <= n.
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4
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0, 2, 1, 4, 3, 2, 6, 5, 4, 3, 8, 7, 6, 5, 4, 10, 9, 8, 7, 6, 5, 12, 11, 10, 9, 8, 7, 6, 14, 13, 12, 11, 10, 9, 8, 7, 16, 15, 14, 13, 12, 11, 10, 9, 8, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n, k) = 2*n - k, 0 <= k <= n.
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EXAMPLE
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Triangle begins:
0;
2, 1;
4, 3, 2;
6, 5, 4, 3;
8, 7, 6, 5, 4;
10, 9, 8, 7, 6, 5;
12, 11, 10, 9, 8, 7, 6;
14, 13, 12, 11, 10, 9, 8, 7;
16, 15, 14, 13, 12, 11, 10, 9, 8;
18, 17, 16, 15, 14, 13, 12, 11, 10, 9;
20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10;
...
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MATHEMATICA
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Column[Table[2*n-k, {n, 0, 10}, {k, 0, n}], Center]
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PROG
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(Python)
def f(x):
a=[]
for k in range(x):
for m in range (k+1):
a.append(2*k-m)
return a
print(f(10))
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CROSSREFS
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T(n, 2*m) = A005843(n), n >= m >= 0 (even-indexed columns).
T(n, 2*m+1) = A005408(n), n >= m >= 0 (odd-indexed columns).
T(n, n-m) = A001477(n+m), n >= m >= 0 (diagonals m >= 0).
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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