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A211990
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Triangle read by rows: T(n,k) = total number of regions in the last k shells of n.
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1
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1, 1, 2, 1, 2, 3, 2, 3, 4, 5, 2, 4, 5, 6, 7, 4, 6, 8, 9, 10, 11, 4, 8, 10, 12, 13, 14, 15, 7, 11, 15, 17, 19, 20, 21, 22, 8, 15, 19, 23, 25, 27, 28, 29, 30, 12, 20, 27, 31, 35, 37, 39, 40, 41, 42, 14, 26, 34, 41, 45, 49, 51, 53, 54, 55, 56, 21, 35, 47
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OFFSET
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1,3
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COMMENTS
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For the definition of "region of n" see A206437. For the definition of "last section of n" see A135010.
Apparently differs from A027300 at the right border.
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LINKS
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FORMULA
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T(n,k) = Sum_{j=1..k} A187219(n-j+1,1).
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EXAMPLE
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For n = 5 and k = 2 we have that the 4th shell of 5 contains two regions: [2] and [4,2,1,1,1]. Then we can see that the 5th shell of 5 contains two regions: [3] and [5,2,1,1,1,1,1]. Therefore the total number of regions in the last two shells of 5 is T(5,2) = 2+2 = 4 (see illustration in the link section).
Triangle begins:
1;
1, 2;
1, 2, 3;
2, 3, 4, 5;
2, 4, 5, 6, 7;
4, 6, 8, 9, 10, 11;
4, 8, 10, 12, 13, 14, 15;
7, 11, 15, 17, 19, 20, 21, 22;
8, 15, 19, 23, 25, 27, 28, 29, 30;
12, 20, 27, 31, 35, 37, 39, 40, 41, 42;
14, 26, 34, 41, 45, 49, 51, 53, 54, 55, 56;
21, 35, 47, 55, 62, 66, 70, 72, 74, 75, 76, 77;
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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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