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A115723 Table of partitions of n with maximum rectangle k. 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
Eric Weisstein's World of Mathematics, Ferrers Diagram.
FORMULA
Sum_{k=1..n} k * T(n,k) = A182099(n).
EXAMPLE
The table starts:
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;
...
CROSSREFS
Cf. A000005 (diagonal), A000041 (row sums), A061017 (column indices of leftmost nonzero elements), A115724 (column sums), A115727, A115728, A006218, A182099.
Sequence in context: A261249 A058650 A112177 * A238160 A178524 A321731
KEYWORD
nonn,tabl,look
AUTHOR
STATUS
approved

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Last modified April 21 14:03 EDT 2024. Contains 371870 sequences. (Running on oeis4.)