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.

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.

Links

Table of n, a(n) for n=1..78.

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;

Crossrefs

Cf. A006128, A066897, A066898, A135010, A138121, A138135, A138137, A141285, A181187, A182703, A206563, A207031.

Sequence in context: A130028 A129560 A218603 * A169940 A279010 A121481

Adjacent sequences: A207029 A207030 A207031 * A207033 A207034 A207035

Keyword

nonn,tabl

Author

Omar E. Pol, Feb 17 2012

Status

approved