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A207032
Triangle read by rows: T(n,k) = number of odd/even parts >= k in the last section of the set of partitions of n, if k is odd/even.
13
1, 1, 1, 3, 0, 1, 3, 3, 0, 1, 7, 1, 2, 0, 1, 9, 6, 2, 2, 0, 1, 15, 4, 4, 1, 2, 0, 1, 19, 13, 4, 5, 1, 2, 0, 1, 32, 10, 10, 3, 4, 1, 2, 0, 1, 40, 24, 10, 9, 4, 4, 1, 2, 0, 1, 60, 23, 18, 8, 8, 3, 4, 1, 2, 0, 1, 78, 46, 22, 19, 8, 9, 3, 4, 1, 2, 0, 1
OFFSET
1,4
COMMENTS
For the calculation of row n, the number of odd/even parts, etc, take the row n from the triangle A207031 and then follow the same rules of A206563.
FORMULA
It appears that T(n,k) = abs(Sum_{j=k..n} (-1)^j*A207031(n,j)).
It appears that A182703(n,k) = T(n,k) - T(n,k+2). - Omar E. Pol, Feb 26 2012
EXAMPLE
Triangle begins:
1;
1, 1;
3, 0, 1;
3, 3, 0, 1;
7, 1, 2, 0, 1;
9, 6, 2, 2, 0, 1;
15, 4, 4, 1, 2, 0, 1;
19, 13, 4, 5, 1, 2, 0, 1;
32, 10, 10, 3, 4, 1, 2, 0, 1;
40, 24, 10, 9, 4, 4, 1, 2, 0, 1;
60, 23, 18, 8, 8, 3, 4, 1, 2, 0, 1;
78, 46, 22, 19, 8, 9, 3, 4, 1, 2, 0, 1;
KEYWORD
nonn,tabl,changed
AUTHOR
Omar E. Pol, Feb 17 2012
STATUS
approved