|
| |
|
|
A069713
|
|
As a square array T(n,k) by antidiagonals, number of ways of partitioning k into up to n parts each no more than 5, or into up to 5 parts each no more than n; as a triangle t(n,k), number of ways of partitioning n into exactly k parts each no more than 6 (i.e., of arranging k indistinguishable standard dice to produce a total of n).
|
|
1
|
|
|
|
1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 3, 3, 2, 1, 1, 0, 0, 3, 4, 3, 2, 1, 1, 0, 0, 3, 5, 5, 3, 2, 1, 1, 0, 0, 2, 6, 6, 5, 3, 2, 1, 1, 0, 0, 2, 6, 8, 7, 5, 3, 2, 1, 1, 0, 0, 1, 6, 9, 9, 7, 5, 3, 2, 1, 1, 0, 0, 1, 6, 11, 11, 10, 7, 5, 3, 2, 1, 1, 0, 0, 0, 5, 11, 14, 12, 10, 7, 5
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,13
|
|
|
LINKS
|
|
|
|
FORMULA
|
If k<6 T(n,k) = A068914(n,k). T(n,k) = T(n,5n-k); t(n,k) = t(7n-k,k). T(floor(5n/2),n) = t(n,floor(7n/2)) = A001975(n).
|
|
|
EXAMPLE
|
As square array, rows start: 1,0,0,0,0,0,...; 1,1,1,1,1,1,...; 1,1,2,2,3,3,...; 1,1,2,3,4,5,...; 1,1,2,3,5,6,...; 1,1,2,3,5,7,...; etc. As triangle, rows start: 1; 0,1; 0,1,1; 0,1,1,1; 0,1,2,1,1; 0,1,2,2,1,1; 0,1,3,3,2,1,1; etc. T(3,7)=6 since 7 can be written as 5+2, 5+1+1, 4+3, 4+2+1, 3+3+1, 3+2+2; or alternatively as 2+2+1+1+1, 3+1+1+1, 2+2+2+1, 3+2+1+1, 3+2+2, 3+3+1. t(10,3)=6 since 10 can be written as 6+3+1, 6+2+2, 5+4+1, 5+3+2, 4+4+2, 4+3+3.
|
|
|
CROSSREFS
|
Cf. A061676 for a similar triangle, though with distinguishable dice (and a different offset). Antidiagonal sums of T(n, k), i.e., row sums (over k) of t(n, k), are A001402. First 22 terms are same as A068914 (see formula).
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
