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A307239
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Analog of Pascal's triangle, with A007947 applied to each sum.
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2
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 6, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 5, 2, 5, 2, 1, 1, 3, 7, 7, 7, 7, 3, 1, 1, 2, 10, 14, 14, 14, 10, 2, 1, 1, 3, 6, 6, 14, 14, 6, 6, 3, 1, 1, 2, 3, 6, 10, 14, 10, 6, 3, 2, 1, 1, 3, 5, 3, 2, 6, 6, 2, 3, 5, 3, 1, 1, 2, 2, 2, 5, 2, 6, 2, 5, 2, 2, 2, 1
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OFFSET
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0,5
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COMMENTS
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The parity of the terms in this triangle is the same as in Pascal's triangle (A007318). As a consequence, the number of odd terms in row n is A001316(n).
The distribution of the terms different from 2 in the triangle evokes Sierpinski's triangle; this is also the case for terms that are multiples of 3 (see illustrations in Links section).
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LINKS
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EXAMPLE
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Triangle begins:
0: 1
1: 1 1
2: 1 2 1
3: 1 3 3 1
4: 1 2 6 2 1
5: 1 3 2 2 3 1
6: 1 2 5 2 5 2 1
7: 1 3 7 7 7 7 3 1
8: 1 2 10 14 14 14 10 2 1
9: 1 3 6 6 14 14 6 6 3 1
...
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PROG
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(PARI) rad(n) = my (p=factor(n)[, 1]~); prod(i=1, #p, p[i])
{ for (r=0, 12, row = vector(r+1, k, if ( k==1||k==r+1, 1, rad(row[k-1]+row[k]))); for (c=1, #row, print1 (row[c] ", "))) }
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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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