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A187881
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Triangle read by rows: the n-th column consists of n n's followed by 0's.
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0
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1, 0, 2, 0, 2, 3, 0, 0, 3, 4, 0, 0, 3, 4, 5, 0, 0, 0, 4, 5, 6, 0, 0, 0, 4, 5, 6, 7, 0, 0, 0, 0, 5, 6, 7, 8, 0, 0, 0, 0, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 11
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OFFSET
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1,3
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COMMENTS
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Row sums = A001318: (1, 2, 5, 7, 12,...)
The triangle is a variant of Janet's periodic table:
.......1
.......2
.....2,3
.....3,4
...3,4,5
...4,5,6
.4,5,6,7
.5,6,7,8
...
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LINKS
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FORMULA
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As an infinite lower triangular matrix, A * B, where A = A101688 and B = an infinite lower triangular matrix with (1, 2, 3,...) as the main diagonal and the rest zeros.
a(n) = floor((2*n-t*(t+1)+1)/(t+3))*(n-t*(t+1)/2), 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
0, 2
0, 2, 3
0, 0, 3, 4
0, 0, 3, 4, 5
0, 0, 0, 4, 5, 6
0, 0, 0, 4, 5, 6, 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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