|
|
A143786
|
|
Number of arithmetic progressions from m to n; a rectangular array, m>=0, n>=0, by antidiagonals.
|
|
0
|
|
|
1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 3, 2, 1, 2, 3, 2, 2, 1, 1, 2, 2, 4, 3, 2, 1, 2, 3, 4, 2, 2, 2, 1, 1, 2, 2, 2, 4, 4, 3, 2, 1, 2, 3, 4, 4, 3, 2, 2, 2, 1, 1, 2, 2, 2, 3, 4, 4, 4, 3, 2, 1, 2, 3, 4, 4, 4, 2, 3, 2, 2, 2, 1, 1, 2, 2, 2, 3, 2, 6, 4, 4, 4, 3, 2, 1, 2, 3, 4, 4, 4, 6, 2, 2, 3, 2, 2, 2, 1, 1, 2, 2, 2, 3, 2, 2
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
T(m,n) = number of solutions (h,k) of n=m+hk, where h>=0, k>=0. Except for initial terms every row (and column) is A000005.
|
|
LINKS
|
|
|
EXAMPLE
|
Northwest corner:
1 1 2 2 3 2 4
1 1 1 2 2 3 2
2 1 1 1 2 2 3
2 2 1 1 1 2 2
3 2 2 1 1 1 2
T(8,2) counts these 4 arithmetic progressions:
2,3,4,5,6,7,8; 2,4,6,8; 2,5,8; and 2,8.
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|