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A218907 Triangle, read by rows, of integer partitions of n by kernel size k. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 11:51 EDT 2021. Contains 348150 sequences. (Running on oeis4.)