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1, 4, 2, 7, 5, 3, 10, 8, 6, 4, 13, 11, 9, 7, 5, 16, 14, 12, 10, 8, 6, 19, 17, 15, 13, 11, 9, 7, 22, 20, 18, 16, 14, 12, 10, 8, 25, 23, 21, 19, 17, 15, 13, 11, 9, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10
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OFFSET
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1,2
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COMMENTS
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Row sums = the hexagonal numbers, A000384: (1, 6, 15, 28, 45, ...).
Table T(n,k) = n + 3*k - 3, n, k > 0, read by antidiagonals. General case A209304. Let m be a positive integer. The first column of the table T(n,1) is the sequence of the positive integers A000027. Every subsequent column is formed from the previous column, shifted by m elements.
for m=4 the result is A209304. (End)
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LINKS
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FORMULA
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For the general case
a(n) = m*(t+1) + (m-1)*(t*(t+1)/2-n), where t = floor((-1+sqrt(8*n-7))/2).
For m = 3,
a(n) = 3*(t+1) + 2*(t*(t+1)/2-n), where t = floor((-1+sqrt(8*n-7))/2). (End)
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EXAMPLE
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First few rows of the triangle:
1;
4, 2;
7, 5, 3;
10, 8, 6, 4;
13, 11, 9, 7, 5;
16, 14, 12, 10, 8, 6;
19, 17, 15, 13, 11, 9, 7;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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