A218907 Triangle, read by rows, of integer partitions of n by kernel size k.

1, 2, 0, 2, 0, 1, 2, 0, 2, 1, 2, 0, 2, 2, 1, 2, 0, 2, 4, 2, 1, 2, 0, 2, 4, 2, 4, 1, 2, 0, 2, 6, 2, 6, 2, 2, 2, 0, 2, 6, 2, 8, 2, 6, 2, 2, 0, 2, 8, 2, 8, 2, 12, 4, 2, 2, 0, 2, 8, 2, 10, 2, 14, 6, 8, 2, 2, 0, 2, 10, 2, 10, 2, 18, 8, 14, 6, 3, 2, 0, 2, 10, 2, 12, 2, 18, 10, 20, 10, 10, 3, 2, 0, 2, 12, 2, 12, 2, 22, 12, 22, 14, 20, 10, 3, 2, 0, 2, 12, 2, 14, 2, 22, 16, 26, 16, 26, 20, 12, 4

Offset

1,2

Comments

Row sum is A000041.

Sum k*T(n,k) = A208914(n).

The kernel of an integer partition is the intersection of its Ferrers diagram and of the Ferrers diagram of its conjugate.

Its size is between 1 (for an all-1 partition) and n (for a self-conjugate partition).

Links

Table of n, a(n) for n=1..120.

Example

Triangle begins:
1;
2, 0;
2, 0, 1;
2, 0, 2,  1;
2, 0, 2,  2, 1;
2, 0, 2,  4, 2,  1;
2, 0, 2,  4, 2,  4, 1;
2, 0, 2,  6, 2,  6, 2,  2;
2, 0, 2,  6, 2,  8, 2,  6,  2;
2, 0, 2,  8, 2,  8, 2, 12,  4,  2;
2, 0, 2,  8, 2, 10, 2, 14,  6,  8,  2;
2, 0, 2, 10, 2, 10, 2, 18,  8, 14,  6,  3;
2, 0, 2, 10, 2, 12, 2, 18, 10, 20, 10, 10, 3;
2, 0, 2, 12, 2, 12, 2, 22, 12, 22, 14, 20, 10, 3;
2, 0, 2, 12, 2, 14, 2, 22, 16, 26, 16, 26, 20, 12, 4;

Crossrefs

Cf. A218904, A218905, A218906.

Cf. A115720, A115994, A246581.

Main diagonal gives A000700.

Sequence in context: A245718 A192011 A152855 * A192575 A029401 A086150

Adjacent sequences: A218904 A218905 A218906 * A218908 A218909 A218910

Keyword

nonn,tabl

Author

Olivier Gérard, Nov 08 2012

Status

approved