A068906 Square array read by ascending antidiagonals of partitions of k modulo n.

0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 1, 1, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 0, 0, 3, 2, 5, 3, 2, 1, 0, 0, 1, 3, 1, 1, 5, 3, 2, 1, 0, 0, 0, 2, 0, 5, 0, 5, 3, 2, 1, 0, 0, 0, 2, 2, 3, 4, 7, 5, 3, 2, 1, 0, 1, 2, 2, 0, 4, 1, 3, 7, 5, 3, 2, 1, 0, 1, 2, 0, 2, 0, 1, 7, 2, 7, 5, 3, 2, 1

Offset

1,9

Comments

0 is disproportionately common modulo 5, 7 and 11, largely because T(5,5m+4)=T(7,7m+5)=T(11,11m+6)=0.

Links

Table of n, a(n) for n=1..105.

Henry Bottomley, Partition calculators using java applets

Index entries for sequences related to partitions

Formula

T(n, k) =A051127(n, A000041(k))

Example

Rows start 0,0,0,0,0,...; 1,0,1,1,1,...; 1,2,0,2,1,...; 1,2,3,1,3,...; 1,2,3,0,2,1,...; 1,2,3,5,1,5,...; 1,2,3,5,0,...; 1,2,3,5,7,...; etc.

Crossrefs

Rows 2, 3, 5, 7 and 11 give A040051, A068907, A068908, A068909, A020919.

Sequence in context: A115672 A079694 A339895 * A162514 A364039 A166347

Adjacent sequences: A068903 A068904 A068905 * A068907 A068908 A068909

Keyword

nonn,tabl

Author

Henry Bottomley, Mar 05 2002

Status

approved