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A068606 Square table by antidiagonals of T(n,k)=n*k*(n+k+1). 3
0, 0, 0, 0, 3, 0, 0, 8, 8, 0, 0, 15, 20, 15, 0, 0, 24, 36, 36, 24, 0, 0, 35, 56, 63, 56, 35, 0, 0, 48, 80, 96, 96, 80, 48, 0, 0, 63, 108, 135, 144, 135, 108, 63, 0, 0, 80, 140, 180, 200, 200, 180, 140, 80, 0, 0, 99, 176, 231, 264, 275, 264, 231, 176, 99, 0, 0, 120, 216, 288 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Considering partitions with up to n positive integers each no more than k (or equivalently paths of length n+k from one corner to the opposite corner of an n*k rectangle) there are C(n+k,n) such partitions (or paths); the mean of the sums of the partitions (or mean of the areas above the paths) is nk/2; and the variance of the sums of the partitions (or variance of the areas above the paths) is a(n)/12.

LINKS

Table of n, a(n) for n=0..69.

EXAMPLE

Rows start:

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

0,3,8,15,24,...;

0,8,20,36,56,...;

0,15,36,63,96,...;

etc.

CROSSREFS

Cf. A068607 for the same table as a triangle.

Sequence in context: A346879 A326397 A140577 * A106153 A166244 A022001

Adjacent sequences:  A068603 A068604 A068605 * A068607 A068608 A068609

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Feb 24 2002

STATUS

approved

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Last modified January 22 00:08 EST 2022. Contains 350481 sequences. (Running on oeis4.)