A182099 -id:A182099

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A115723

Table of partitions of n with maximum rectangle k.

+10
4

1, 0, 2, 0, 1, 2, 0, 0, 2, 3, 0, 0, 1, 4, 2, 0, 0, 0, 5, 2, 4, 0, 0, 0, 3, 4, 6, 2, 0, 0, 0, 1, 4, 11, 2, 4, 0, 0, 0, 0, 3, 14, 4, 6, 3, 0, 0, 0, 0, 1, 15, 6, 12, 4, 4, 0, 0, 0, 0, 0, 13, 8, 18, 9, 6, 2, 0, 0, 0, 0, 0, 8, 10, 25, 14, 12, 2, 6, 0, 0, 0, 0, 0, 4, 9, 30, 22, 20, 4, 10, 2

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

T(n,k)=0 if n > A006218(k).

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

Eric Weisstein's World of Mathematics, Ferrers Diagram.

FORMULA

Sum_{k=1..n} k * T(n,k) = A182099(n).

EXAMPLE

The table starts:

0, 2;

0, 1, 2;

0, 0, 2, 3;

0, 0, 1, 4, 2;

0, 0, 0, 5, 2, 4;

0, 0, 0, 3, 4, 6, 2;

0, 0, 0, 1, 4, 11, 2, 4;

0, 0, 0, 0, 3, 14, 4, 6, 3;

0, 0, 0, 0, 1, 15, 6, 12, 4, 4;

...

CROSSREFS

Cf. A000005 (diagonal), A000041 (row sums), A061017 (column indices of leftmost nonzero elements), A115724 (column sums), A115727, A115728, A006218, A182099.

KEYWORD

nonn,tabl,look

AUTHOR

Franklin T. Adams-Watters, Mar 11 2006

STATUS

approved

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