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A211990
Triangle read by rows: T(n,k) = total number of regions in the last k shells of n.
1
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
OFFSET
1,3
COMMENTS
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.
FORMULA
T(n,k) = A000041(n) - A000041(n-k), if 1<k<n.
T(n,k) = A000041(n), if k = n.
T(n,k) = Sum_{j=1..k} A187219(n-j+1,1).
EXAMPLE
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;
CROSSREFS
Mirror of triangle A211980. Column 1 is A187219. Right border gives A000041, n >= 1.
Sequence in context: A025798 A161064 A070086 * A162618 A036576 A171729
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Apr 27 2012
STATUS
approved