A143786 Number of arithmetic progressions from m to n; a rectangular array, m>=0, n>=0, by antidiagonals.

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

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

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

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

Cf. A000005.

Sequence in context: A272772 A293431 A078573 * A232353 A366987 A304093

Adjacent sequences: A143783 A143784 A143785 * A143787 A143788 A143789

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 01 2008

Status

approved