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A070936 Square array read by antidiagonals: T(n,k) = number of partitions of n into distinct parts, each no more than k. 4
1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 1, 2, 1, 0, 0, 0, 1, 1, 1, 2, 2, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 3, 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 3, 1, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,25

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Henry Bottomley, Partition calculators using java applets

Index entries for sequences related to partitions

FORMULA

T(n, k) =T(n-1, k)+T(n-1, k-n) (with T(0, 0)=1) =A053632(k, n) =A026836(n+k+1, k+1) =sum_{0<=j<=k}A026836(n, j). For k>=n, T(n, k)=T(n, n)=A000009(n).

EXAMPLE

Rows start

1,1,1,1,1,...;

0,1,1,1,1,...;

0,0,1,1,1,...;

0,0,1,2,2,...;

0,0,0,1,2,...; etc.

T(10,5)=3 since 10 can be partitioned 3 ways as 5+4+1=5+3+2=4+3+2+1 with each part less than or equal to 5.

CROSSREFS

Cf. A008284, A060016. With some imagination, this is the transpose of A026836 and A053632. Column sums are 2^k=A000079(k). Column maximum is A025591(k), which appears A070936(k) times in the column.

Sequence in context: A129753 A307247 A147693 * A014081 A091890 A029431

Adjacent sequences:  A070933 A070934 A070935 * A070937 A070938 A070939

KEYWORD

nonn,tabl,look

AUTHOR

Henry Bottomley, May 12 2002

STATUS

approved

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Last modified March 3 12:16 EST 2021. Contains 341762 sequences. (Running on oeis4.)