A068606 Square table by antidiagonals of T(n,k)=n*k*(n+k+1).

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

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